ARIMA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c0fa0de6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sms\n",
    "import pandas as pd\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d532053e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Month</th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1949-01</td>\n",
       "      <td>112.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1949-02</td>\n",
       "      <td>118.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1949-03</td>\n",
       "      <td>132.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1949-04</td>\n",
       "      <td>129.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1949-05</td>\n",
       "      <td>121.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Month  Thousands of Passengers\n",
       "0  1949-01                    112.0\n",
       "1  1949-02                    118.0\n",
       "2  1949-03                    132.0\n",
       "3  1949-04                    129.0\n",
       "4  1949-05                    121.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_airline=pd.read_csv('airline_passengers.csv')\n",
    "df_airline.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9298f379",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Month                      0\n",
       "Thousands of Passengers    1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_airline.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8c0046d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Month</th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>140</th>\n",
       "      <td>1960-09</td>\n",
       "      <td>508.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>1960-10</td>\n",
       "      <td>461.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>142</th>\n",
       "      <td>1960-11</td>\n",
       "      <td>390.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>143</th>\n",
       "      <td>1960-12</td>\n",
       "      <td>432.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>144</th>\n",
       "      <td>International airline passengers: monthly tota...</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 Month  \\\n",
       "140                                            1960-09   \n",
       "141                                            1960-10   \n",
       "142                                            1960-11   \n",
       "143                                            1960-12   \n",
       "144  International airline passengers: monthly tota...   \n",
       "\n",
       "     Thousands of Passengers  \n",
       "140                    508.0  \n",
       "141                    461.0  \n",
       "142                    390.0  \n",
       "143                    432.0  \n",
       "144                      NaN  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_airline.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9b647cd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_airline.dropna(axis=0,inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a07efb56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Month                      0\n",
       "Thousands of Passengers    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_airline.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "45edd7ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 144 entries, 0 to 143\n",
      "Data columns (total 2 columns):\n",
      " #   Column                   Non-Null Count  Dtype  \n",
      "---  ------                   --------------  -----  \n",
      " 0   Month                    144 non-null    object \n",
      " 1   Thousands of Passengers  144 non-null    float64\n",
      "dtypes: float64(1), object(1)\n",
      "memory usage: 3.4+ KB\n"
     ]
    }
   ],
   "source": [
    "df_airline.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "150dfa4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_airline['Month']=pd.to_datetime(df_airline['Month'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9f031ae8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 144 entries, 0 to 143\n",
      "Data columns (total 2 columns):\n",
      " #   Column                   Non-Null Count  Dtype         \n",
      "---  ------                   --------------  -----         \n",
      " 0   Month                    144 non-null    datetime64[ns]\n",
      " 1   Thousands of Passengers  144 non-null    float64       \n",
      "dtypes: datetime64[ns](1), float64(1)\n",
      "memory usage: 3.4 KB\n"
     ]
    }
   ],
   "source": [
    "df_airline.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ad74c0e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Month</th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1949-01-01</td>\n",
       "      <td>112.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1949-02-01</td>\n",
       "      <td>118.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1949-03-01</td>\n",
       "      <td>132.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1949-04-01</td>\n",
       "      <td>129.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1949-05-01</td>\n",
       "      <td>121.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Month  Thousands of Passengers\n",
       "0 1949-01-01                    112.0\n",
       "1 1949-02-01                    118.0\n",
       "2 1949-03-01                    132.0\n",
       "3 1949-04-01                    129.0\n",
       "4 1949-05-01                    121.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_airline.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1b5d6bb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_airline.set_index('Month',inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "56f64765",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>112.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>132.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>129.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>121.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Thousands of Passengers\n",
       "Month                              \n",
       "1949-01-01                    112.0\n",
       "1949-02-01                    118.0\n",
       "1949-03-01                    132.0\n",
       "1949-04-01                    129.0\n",
       "1949-05-01                    121.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_airline.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fd83f7a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Month'>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_airline.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "31334a4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tsa.stattools import adfuller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "88c9760d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def adf_test(series):\n",
    "    result=adfuller(series)\n",
    "    print('ADF Statistics: {}'.format(result[0]))\n",
    "    print('p- value: {}'.format(result[1]))\n",
    "    if result[1] <= 0.05:\n",
    "        print(\"strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\")\n",
    "    else:\n",
    "        print(\"weak evidence against null hypothesis, time series has a unit root, indicating it is non-stationary \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5487bf1e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistics: 0.8153688792060511\n",
      "p- value: 0.991880243437641\n",
      "weak evidence against null hypothesis, time series has a unit root, indicating it is non-stationary \n"
     ]
    }
   ],
   "source": [
    "adf_test(df_airline['Thousands of Passengers'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7b632838",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Use Techniques Differencing\n",
    "df_airline['Passengers First Difference']=df_airline['Thousands of Passengers']-df_airline['Thousands of Passengers'].shift(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9dd11d67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "      <th>Passengers First Difference</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>112.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>132.0</td>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>129.0</td>\n",
       "      <td>-3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>121.0</td>\n",
       "      <td>-8.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Thousands of Passengers  Passengers First Difference\n",
       "Month                                                           \n",
       "1949-01-01                    112.0                          NaN\n",
       "1949-02-01                    118.0                          6.0\n",
       "1949-03-01                    132.0                         14.0\n",
       "1949-04-01                    129.0                         -3.0\n",
       "1949-05-01                    121.0                         -8.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_airline.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c80a6972",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistics: -2.8292668241699883\n",
      "p- value: 0.054213290283826945\n",
      "weak evidence against null hypothesis, time series has a unit root, indicating it is non-stationary \n"
     ]
    }
   ],
   "source": [
    "adf_test(df_airline['Passengers First Difference'].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8c10bc6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Use Techniques Differencing\n",
    "df_airline['Passengers Second Difference']=df_airline['Passengers First Difference']-df_airline['Passengers First Difference'].shift(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "40ebf2aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistics: -16.384231542468527\n",
      "p- value: 2.732891850014085e-29\n",
      "strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\n"
     ]
    }
   ],
   "source": [
    "adf_test(df_airline['Passengers Second Difference'].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "67d483db",
   "metadata": {},
   "outputs": [],
   "source": [
    "### 12 months \n",
    "## Use Techniques Differencing\n",
    "df_airline['Passengers 12 Difference']=df_airline['Thousands of Passengers']-df_airline['Thousands of Passengers'].shift(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "811d1a28",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistics: -3.3830207264924796\n",
      "p- value: 0.011551493085515008\n",
      "strong evidence against the null hypothesis, reject the null hypothesis. Data has no unit root and is stationary\n"
     ]
    }
   ],
   "source": [
    "adf_test(df_airline['Passengers 12 Difference'].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ebb905a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf,plot_pacf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1071b3bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf = plot_acf(df_airline[\"Passengers Second Difference\"].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2ec86f92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf12 = plot_acf(df_airline[\"Passengers 12 Difference\"].dropna())\n",
    "pacf12 = plot_pacf(df_airline[\"Passengers 12 Difference\"].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "5a378cfc",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\win10\\anaconda3\\lib\\site-packages\\statsmodels\\regression\\linear_model.py:1434: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return rho, np.sqrt(sigmasq)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = plot_pacf(df_airline[\"Passengers Second Difference\"].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "62367b3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pacf12 = plot_pacf(df_airline[\"Passengers 12 Difference\"].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e21a81db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "      <th>Passengers First Difference</th>\n",
       "      <th>Passengers Second Difference</th>\n",
       "      <th>Passengers 12 Difference</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>112.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>132.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>129.0</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>-17.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>121.0</td>\n",
       "      <td>-8.0</td>\n",
       "      <td>-5.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-08-01</th>\n",
       "      <td>606.0</td>\n",
       "      <td>-16.0</td>\n",
       "      <td>-103.0</td>\n",
       "      <td>47.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-09-01</th>\n",
       "      <td>508.0</td>\n",
       "      <td>-98.0</td>\n",
       "      <td>-82.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-10-01</th>\n",
       "      <td>461.0</td>\n",
       "      <td>-47.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>54.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-11-01</th>\n",
       "      <td>390.0</td>\n",
       "      <td>-71.0</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>28.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-12-01</th>\n",
       "      <td>432.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>113.0</td>\n",
       "      <td>27.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>144 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Thousands of Passengers  Passengers First Difference  \\\n",
       "Month                                                              \n",
       "1949-01-01                    112.0                          NaN   \n",
       "1949-02-01                    118.0                          6.0   \n",
       "1949-03-01                    132.0                         14.0   \n",
       "1949-04-01                    129.0                         -3.0   \n",
       "1949-05-01                    121.0                         -8.0   \n",
       "...                             ...                          ...   \n",
       "1960-08-01                    606.0                        -16.0   \n",
       "1960-09-01                    508.0                        -98.0   \n",
       "1960-10-01                    461.0                        -47.0   \n",
       "1960-11-01                    390.0                        -71.0   \n",
       "1960-12-01                    432.0                         42.0   \n",
       "\n",
       "            Passengers Second Difference  Passengers 12 Difference  \n",
       "Month                                                               \n",
       "1949-01-01                           NaN                       NaN  \n",
       "1949-02-01                           NaN                       NaN  \n",
       "1949-03-01                           8.0                       NaN  \n",
       "1949-04-01                         -17.0                       NaN  \n",
       "1949-05-01                          -5.0                       NaN  \n",
       "...                                  ...                       ...  \n",
       "1960-08-01                        -103.0                      47.0  \n",
       "1960-09-01                         -82.0                      45.0  \n",
       "1960-10-01                          51.0                      54.0  \n",
       "1960-11-01                         -24.0                      28.0  \n",
       "1960-12-01                         113.0                      27.0  \n",
       "\n",
       "[144 rows x 4 columns]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### split train and test data\n",
    "df_airline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "0f8a1ab0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from datetime import datetime,timedelta\n",
    "train_dataset_end=datetime(1955,12,1)\n",
    "test_dataset_end=datetime(1960,12,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "9f4012f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data=df_airline[:train_dataset_end]\n",
    "test_data=df_airline[train_dataset_end+timedelta(days=1):test_dataset_end]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "f15a58e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "##prediction\n",
    "pred_start_date=test_data.index[0]\n",
    "pred_end_date=test_data.index[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e0317954",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "      <th>Passengers First Difference</th>\n",
       "      <th>Passengers Second Difference</th>\n",
       "      <th>Passengers 12 Difference</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1956-01-01</th>\n",
       "      <td>284.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>-35.0</td>\n",
       "      <td>42.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-02-01</th>\n",
       "      <td>277.0</td>\n",
       "      <td>-7.0</td>\n",
       "      <td>-13.0</td>\n",
       "      <td>44.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-03-01</th>\n",
       "      <td>317.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>50.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-04-01</th>\n",
       "      <td>313.0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>-44.0</td>\n",
       "      <td>44.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-05-01</th>\n",
       "      <td>318.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>48.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-06-01</th>\n",
       "      <td>374.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>59.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-07-01</th>\n",
       "      <td>413.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>-17.0</td>\n",
       "      <td>49.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-08-01</th>\n",
       "      <td>405.0</td>\n",
       "      <td>-8.0</td>\n",
       "      <td>-47.0</td>\n",
       "      <td>58.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-09-01</th>\n",
       "      <td>355.0</td>\n",
       "      <td>-50.0</td>\n",
       "      <td>-42.0</td>\n",
       "      <td>43.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-10-01</th>\n",
       "      <td>306.0</td>\n",
       "      <td>-49.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>32.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-11-01</th>\n",
       "      <td>271.0</td>\n",
       "      <td>-35.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>34.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-12-01</th>\n",
       "      <td>306.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>28.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-01-01</th>\n",
       "      <td>315.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>-26.0</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-02-01</th>\n",
       "      <td>301.0</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>-23.0</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-03-01</th>\n",
       "      <td>356.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>39.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-04-01</th>\n",
       "      <td>348.0</td>\n",
       "      <td>-8.0</td>\n",
       "      <td>-63.0</td>\n",
       "      <td>35.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-05-01</th>\n",
       "      <td>355.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-06-01</th>\n",
       "      <td>422.0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>48.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-07-01</th>\n",
       "      <td>465.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-08-01</th>\n",
       "      <td>467.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>-41.0</td>\n",
       "      <td>62.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-09-01</th>\n",
       "      <td>404.0</td>\n",
       "      <td>-63.0</td>\n",
       "      <td>-65.0</td>\n",
       "      <td>49.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-10-01</th>\n",
       "      <td>347.0</td>\n",
       "      <td>-57.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-11-01</th>\n",
       "      <td>305.0</td>\n",
       "      <td>-42.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>34.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-12-01</th>\n",
       "      <td>336.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>73.0</td>\n",
       "      <td>30.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-01-01</th>\n",
       "      <td>340.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-27.0</td>\n",
       "      <td>25.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-02-01</th>\n",
       "      <td>318.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>-26.0</td>\n",
       "      <td>17.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-03-01</th>\n",
       "      <td>362.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-04-01</th>\n",
       "      <td>348.0</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>-58.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-05-01</th>\n",
       "      <td>363.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-06-01</th>\n",
       "      <td>435.0</td>\n",
       "      <td>72.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-07-01</th>\n",
       "      <td>491.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>-16.0</td>\n",
       "      <td>26.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-08-01</th>\n",
       "      <td>505.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>-42.0</td>\n",
       "      <td>38.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-09-01</th>\n",
       "      <td>404.0</td>\n",
       "      <td>-101.0</td>\n",
       "      <td>-115.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-10-01</th>\n",
       "      <td>359.0</td>\n",
       "      <td>-45.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-11-01</th>\n",
       "      <td>310.0</td>\n",
       "      <td>-49.0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-12-01</th>\n",
       "      <td>337.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-01-01</th>\n",
       "      <td>360.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-02-01</th>\n",
       "      <td>342.0</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>-41.0</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-03-01</th>\n",
       "      <td>406.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>44.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-04-01</th>\n",
       "      <td>396.0</td>\n",
       "      <td>-10.0</td>\n",
       "      <td>-74.0</td>\n",
       "      <td>48.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-05-01</th>\n",
       "      <td>420.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>57.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-06-01</th>\n",
       "      <td>472.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-07-01</th>\n",
       "      <td>548.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>57.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-08-01</th>\n",
       "      <td>559.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-65.0</td>\n",
       "      <td>54.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-09-01</th>\n",
       "      <td>463.0</td>\n",
       "      <td>-96.0</td>\n",
       "      <td>-107.0</td>\n",
       "      <td>59.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-10-01</th>\n",
       "      <td>407.0</td>\n",
       "      <td>-56.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>48.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-11-01</th>\n",
       "      <td>362.0</td>\n",
       "      <td>-45.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-12-01</th>\n",
       "      <td>405.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>68.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-01-01</th>\n",
       "      <td>417.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>-31.0</td>\n",
       "      <td>57.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-02-01</th>\n",
       "      <td>391.0</td>\n",
       "      <td>-26.0</td>\n",
       "      <td>-38.0</td>\n",
       "      <td>49.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-03-01</th>\n",
       "      <td>419.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-04-01</th>\n",
       "      <td>461.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>65.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-05-01</th>\n",
       "      <td>472.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-31.0</td>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-06-01</th>\n",
       "      <td>535.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>63.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-07-01</th>\n",
       "      <td>622.0</td>\n",
       "      <td>87.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>74.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-08-01</th>\n",
       "      <td>606.0</td>\n",
       "      <td>-16.0</td>\n",
       "      <td>-103.0</td>\n",
       "      <td>47.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-09-01</th>\n",
       "      <td>508.0</td>\n",
       "      <td>-98.0</td>\n",
       "      <td>-82.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-10-01</th>\n",
       "      <td>461.0</td>\n",
       "      <td>-47.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>54.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-11-01</th>\n",
       "      <td>390.0</td>\n",
       "      <td>-71.0</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>28.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-12-01</th>\n",
       "      <td>432.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>113.0</td>\n",
       "      <td>27.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Thousands of Passengers  Passengers First Difference  \\\n",
       "Month                                                              \n",
       "1956-01-01                    284.0                          6.0   \n",
       "1956-02-01                    277.0                         -7.0   \n",
       "1956-03-01                    317.0                         40.0   \n",
       "1956-04-01                    313.0                         -4.0   \n",
       "1956-05-01                    318.0                          5.0   \n",
       "1956-06-01                    374.0                         56.0   \n",
       "1956-07-01                    413.0                         39.0   \n",
       "1956-08-01                    405.0                         -8.0   \n",
       "1956-09-01                    355.0                        -50.0   \n",
       "1956-10-01                    306.0                        -49.0   \n",
       "1956-11-01                    271.0                        -35.0   \n",
       "1956-12-01                    306.0                         35.0   \n",
       "1957-01-01                    315.0                          9.0   \n",
       "1957-02-01                    301.0                        -14.0   \n",
       "1957-03-01                    356.0                         55.0   \n",
       "1957-04-01                    348.0                         -8.0   \n",
       "1957-05-01                    355.0                          7.0   \n",
       "1957-06-01                    422.0                         67.0   \n",
       "1957-07-01                    465.0                         43.0   \n",
       "1957-08-01                    467.0                          2.0   \n",
       "1957-09-01                    404.0                        -63.0   \n",
       "1957-10-01                    347.0                        -57.0   \n",
       "1957-11-01                    305.0                        -42.0   \n",
       "1957-12-01                    336.0                         31.0   \n",
       "1958-01-01                    340.0                          4.0   \n",
       "1958-02-01                    318.0                        -22.0   \n",
       "1958-03-01                    362.0                         44.0   \n",
       "1958-04-01                    348.0                        -14.0   \n",
       "1958-05-01                    363.0                         15.0   \n",
       "1958-06-01                    435.0                         72.0   \n",
       "1958-07-01                    491.0                         56.0   \n",
       "1958-08-01                    505.0                         14.0   \n",
       "1958-09-01                    404.0                       -101.0   \n",
       "1958-10-01                    359.0                        -45.0   \n",
       "1958-11-01                    310.0                        -49.0   \n",
       "1958-12-01                    337.0                         27.0   \n",
       "1959-01-01                    360.0                         23.0   \n",
       "1959-02-01                    342.0                        -18.0   \n",
       "1959-03-01                    406.0                         64.0   \n",
       "1959-04-01                    396.0                        -10.0   \n",
       "1959-05-01                    420.0                         24.0   \n",
       "1959-06-01                    472.0                         52.0   \n",
       "1959-07-01                    548.0                         76.0   \n",
       "1959-08-01                    559.0                         11.0   \n",
       "1959-09-01                    463.0                        -96.0   \n",
       "1959-10-01                    407.0                        -56.0   \n",
       "1959-11-01                    362.0                        -45.0   \n",
       "1959-12-01                    405.0                         43.0   \n",
       "1960-01-01                    417.0                         12.0   \n",
       "1960-02-01                    391.0                        -26.0   \n",
       "1960-03-01                    419.0                         28.0   \n",
       "1960-04-01                    461.0                         42.0   \n",
       "1960-05-01                    472.0                         11.0   \n",
       "1960-06-01                    535.0                         63.0   \n",
       "1960-07-01                    622.0                         87.0   \n",
       "1960-08-01                    606.0                        -16.0   \n",
       "1960-09-01                    508.0                        -98.0   \n",
       "1960-10-01                    461.0                        -47.0   \n",
       "1960-11-01                    390.0                        -71.0   \n",
       "1960-12-01                    432.0                         42.0   \n",
       "\n",
       "            Passengers Second Difference  Passengers 12 Difference  \n",
       "Month                                                               \n",
       "1956-01-01                         -35.0                      42.0  \n",
       "1956-02-01                         -13.0                      44.0  \n",
       "1956-03-01                          47.0                      50.0  \n",
       "1956-04-01                         -44.0                      44.0  \n",
       "1956-05-01                           9.0                      48.0  \n",
       "1956-06-01                          51.0                      59.0  \n",
       "1956-07-01                         -17.0                      49.0  \n",
       "1956-08-01                         -47.0                      58.0  \n",
       "1956-09-01                         -42.0                      43.0  \n",
       "1956-10-01                           1.0                      32.0  \n",
       "1956-11-01                          14.0                      34.0  \n",
       "1956-12-01                          70.0                      28.0  \n",
       "1957-01-01                         -26.0                      31.0  \n",
       "1957-02-01                         -23.0                      24.0  \n",
       "1957-03-01                          69.0                      39.0  \n",
       "1957-04-01                         -63.0                      35.0  \n",
       "1957-05-01                          15.0                      37.0  \n",
       "1957-06-01                          60.0                      48.0  \n",
       "1957-07-01                         -24.0                      52.0  \n",
       "1957-08-01                         -41.0                      62.0  \n",
       "1957-09-01                         -65.0                      49.0  \n",
       "1957-10-01                           6.0                      41.0  \n",
       "1957-11-01                          15.0                      34.0  \n",
       "1957-12-01                          73.0                      30.0  \n",
       "1958-01-01                         -27.0                      25.0  \n",
       "1958-02-01                         -26.0                      17.0  \n",
       "1958-03-01                          66.0                       6.0  \n",
       "1958-04-01                         -58.0                       0.0  \n",
       "1958-05-01                          29.0                       8.0  \n",
       "1958-06-01                          57.0                      13.0  \n",
       "1958-07-01                         -16.0                      26.0  \n",
       "1958-08-01                         -42.0                      38.0  \n",
       "1958-09-01                        -115.0                       0.0  \n",
       "1958-10-01                          56.0                      12.0  \n",
       "1958-11-01                          -4.0                       5.0  \n",
       "1958-12-01                          76.0                       1.0  \n",
       "1959-01-01                          -4.0                      20.0  \n",
       "1959-02-01                         -41.0                      24.0  \n",
       "1959-03-01                          82.0                      44.0  \n",
       "1959-04-01                         -74.0                      48.0  \n",
       "1959-05-01                          34.0                      57.0  \n",
       "1959-06-01                          28.0                      37.0  \n",
       "1959-07-01                          24.0                      57.0  \n",
       "1959-08-01                         -65.0                      54.0  \n",
       "1959-09-01                        -107.0                      59.0  \n",
       "1959-10-01                          40.0                      48.0  \n",
       "1959-11-01                          11.0                      52.0  \n",
       "1959-12-01                          88.0                      68.0  \n",
       "1960-01-01                         -31.0                      57.0  \n",
       "1960-02-01                         -38.0                      49.0  \n",
       "1960-03-01                          54.0                      13.0  \n",
       "1960-04-01                          14.0                      65.0  \n",
       "1960-05-01                         -31.0                      52.0  \n",
       "1960-06-01                          52.0                      63.0  \n",
       "1960-07-01                          24.0                      74.0  \n",
       "1960-08-01                        -103.0                      47.0  \n",
       "1960-09-01                         -82.0                      45.0  \n",
       "1960-10-01                          51.0                      54.0  \n",
       "1960-11-01                         -24.0                      28.0  \n",
       "1960-12-01                         113.0                      27.0  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "f9dfdc21",
   "metadata": {},
   "outputs": [],
   "source": [
    "## create a ARIMA model\n",
    "from statsmodels.tsa.arima_model import ARIMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "7bae577b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "      <th>Passengers First Difference</th>\n",
       "      <th>Passengers Second Difference</th>\n",
       "      <th>Passengers 12 Difference</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>112.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>132.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>129.0</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>-17.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>121.0</td>\n",
       "      <td>-8.0</td>\n",
       "      <td>-5.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-08-01</th>\n",
       "      <td>347.0</td>\n",
       "      <td>-17.0</td>\n",
       "      <td>-66.0</td>\n",
       "      <td>54.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-09-01</th>\n",
       "      <td>312.0</td>\n",
       "      <td>-35.0</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>53.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-10-01</th>\n",
       "      <td>274.0</td>\n",
       "      <td>-38.0</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-11-01</th>\n",
       "      <td>237.0</td>\n",
       "      <td>-37.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>34.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1955-12-01</th>\n",
       "      <td>278.0</td>\n",
       "      <td>41.0</td>\n",
       "      <td>78.0</td>\n",
       "      <td>49.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>84 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Thousands of Passengers  Passengers First Difference  \\\n",
       "Month                                                              \n",
       "1949-01-01                    112.0                          NaN   \n",
       "1949-02-01                    118.0                          6.0   \n",
       "1949-03-01                    132.0                         14.0   \n",
       "1949-04-01                    129.0                         -3.0   \n",
       "1949-05-01                    121.0                         -8.0   \n",
       "...                             ...                          ...   \n",
       "1955-08-01                    347.0                        -17.0   \n",
       "1955-09-01                    312.0                        -35.0   \n",
       "1955-10-01                    274.0                        -38.0   \n",
       "1955-11-01                    237.0                        -37.0   \n",
       "1955-12-01                    278.0                         41.0   \n",
       "\n",
       "            Passengers Second Difference  Passengers 12 Difference  \n",
       "Month                                                               \n",
       "1949-01-01                           NaN                       NaN  \n",
       "1949-02-01                           NaN                       NaN  \n",
       "1949-03-01                           8.0                       NaN  \n",
       "1949-04-01                         -17.0                       NaN  \n",
       "1949-05-01                          -5.0                       NaN  \n",
       "...                                  ...                       ...  \n",
       "1955-08-01                         -66.0                      54.0  \n",
       "1955-09-01                         -18.0                      53.0  \n",
       "1955-10-01                          -3.0                      45.0  \n",
       "1955-11-01                           1.0                      34.0  \n",
       "1955-12-01                          78.0                      49.0  \n",
       "\n",
       "[84 rows x 4 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "b7f4a46a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\win10\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\arima_model.py:472: FutureWarning: \n",
      "statsmodels.tsa.arima_model.ARMA and statsmodels.tsa.arima_model.ARIMA have\n",
      "been deprecated in favor of statsmodels.tsa.arima.model.ARIMA (note the .\n",
      "between arima and model) and\n",
      "statsmodels.tsa.SARIMAX. These will be removed after the 0.12 release.\n",
      "\n",
      "statsmodels.tsa.arima.model.ARIMA makes use of the statespace framework and\n",
      "is both well tested and maintained.\n",
      "\n",
      "To silence this warning and continue using ARMA and ARIMA until they are\n",
      "removed, use:\n",
      "\n",
      "import warnings\n",
      "warnings.filterwarnings('ignore', 'statsmodels.tsa.arima_model.ARMA',\n",
      "                        FutureWarning)\n",
      "warnings.filterwarnings('ignore', 'statsmodels.tsa.arima_model.ARIMA',\n",
      "                        FutureWarning)\n",
      "\n",
      "  warnings.warn(ARIMA_DEPRECATION_WARN, FutureWarning)\n",
      "C:\\Users\\win10\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  warnings.warn('No frequency information was'\n",
      "C:\\Users\\win10\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  warnings.warn('No frequency information was'\n"
     ]
    }
   ],
   "source": [
    "model_ARIMA=ARIMA(train_data['Thousands of Passengers'],order=(0,2,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "0357c2fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_Arima_fit=model_ARIMA.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "58b9e11c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARIMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th> <td>D2.Thousands of Passengers</td> <th>  No. Observations:  </th>    <td>82</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>ARIMA(0, 2, 0)</td>       <th>  Log Likelihood     </th> <td>-385.782</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                    <td>css</td>            <th>  S.D. of innovations</th>  <td>26.728</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>               <td>Sun, 27 Feb 2022</td>      <th>  AIC                </th>  <td>775.563</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                   <td>20:13:47</td>          <th>  BIC                </th>  <td>780.377</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>                <td>03-01-1949</td>         <th>  HQIC               </th>  <td>777.496</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                      <td>- 12-01-1955</td>        <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.4268</td> <td>    2.952</td> <td>    0.145</td> <td> 0.885</td> <td>   -5.358</td> <td>    6.212</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 ARIMA Model Results                                  \n",
       "======================================================================================\n",
       "Dep. Variable:     D2.Thousands of Passengers   No. Observations:                   82\n",
       "Model:                         ARIMA(0, 2, 0)   Log Likelihood                -385.782\n",
       "Method:                                   css   S.D. of innovations             26.728\n",
       "Date:                        Sun, 27 Feb 2022   AIC                            775.563\n",
       "Time:                                20:13:47   BIC                            780.377\n",
       "Sample:                            03-01-1949   HQIC                           777.496\n",
       "                                 - 12-01-1955                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.4268      2.952      0.145      0.885      -5.358       6.212\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_Arima_fit.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "ffe6a4d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "      <th>Passengers First Difference</th>\n",
       "      <th>Passengers Second Difference</th>\n",
       "      <th>Passengers 12 Difference</th>\n",
       "      <th>Predicted_ARIMA</th>\n",
       "      <th>Predicted_SARIMA</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1956-01-01</th>\n",
       "      <td>284.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>-35.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>-18.162150</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-02-01</th>\n",
       "      <td>277.0</td>\n",
       "      <td>-7.0</td>\n",
       "      <td>-13.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>-45.477686</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-03-01</th>\n",
       "      <td>317.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>36.823887</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-04-01</th>\n",
       "      <td>313.0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>-44.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>-13.751486</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-05-01</th>\n",
       "      <td>318.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>-24.008603</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-06-01</th>\n",
       "      <td>374.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>47.695447</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-07-01</th>\n",
       "      <td>413.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>-17.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>-17.190004</td>\n",
       "      <td>399.012415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-08-01</th>\n",
       "      <td>405.0</td>\n",
       "      <td>-8.0</td>\n",
       "      <td>-47.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>-31.682662</td>\n",
       "      <td>382.942369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-09-01</th>\n",
       "      <td>355.0</td>\n",
       "      <td>-50.0</td>\n",
       "      <td>-42.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>45.053450</td>\n",
       "      <td>347.541878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-10-01</th>\n",
       "      <td>306.0</td>\n",
       "      <td>-49.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>-14.879861</td>\n",
       "      <td>310.733630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-11-01</th>\n",
       "      <td>271.0</td>\n",
       "      <td>-35.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-29.599343</td>\n",
       "      <td>275.541082</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-12-01</th>\n",
       "      <td>306.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>45.461525</td>\n",
       "      <td>313.142988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-01-01</th>\n",
       "      <td>315.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>-26.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>-15.359948</td>\n",
       "      <td>319.590512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-02-01</th>\n",
       "      <td>301.0</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>-23.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>-30.599654</td>\n",
       "      <td>312.766913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-03-01</th>\n",
       "      <td>356.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>45.359258</td>\n",
       "      <td>344.240377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-04-01</th>\n",
       "      <td>348.0</td>\n",
       "      <td>-8.0</td>\n",
       "      <td>-63.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>-14.685594</td>\n",
       "      <td>344.173943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-05-01</th>\n",
       "      <td>355.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>-30.678062</td>\n",
       "      <td>345.215411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-06-01</th>\n",
       "      <td>422.0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>45.253970</td>\n",
       "      <td>387.676459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-07-01</th>\n",
       "      <td>465.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>-14.443474</td>\n",
       "      <td>434.322457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-08-01</th>\n",
       "      <td>467.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>-41.0</td>\n",
       "      <td>62.0</td>\n",
       "      <td>-31.010197</td>\n",
       "      <td>417.510876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-09-01</th>\n",
       "      <td>404.0</td>\n",
       "      <td>-63.0</td>\n",
       "      <td>-65.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>45.198710</td>\n",
       "      <td>381.686456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-10-01</th>\n",
       "      <td>347.0</td>\n",
       "      <td>-57.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>41.0</td>\n",
       "      <td>-14.048689</td>\n",
       "      <td>344.056058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-11-01</th>\n",
       "      <td>305.0</td>\n",
       "      <td>-42.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-31.275681</td>\n",
       "      <td>307.775441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-12-01</th>\n",
       "      <td>336.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>73.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>45.107187</td>\n",
       "      <td>345.978918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-01-01</th>\n",
       "      <td>340.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-27.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>-13.703068</td>\n",
       "      <td>351.527557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-02-01</th>\n",
       "      <td>318.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>-26.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-31.553004</td>\n",
       "      <td>344.523221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-03-01</th>\n",
       "      <td>362.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>45.028083</td>\n",
       "      <td>375.622211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-04-01</th>\n",
       "      <td>348.0</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>-58.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-13.340926</td>\n",
       "      <td>375.020011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-05-01</th>\n",
       "      <td>363.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>-31.826277</td>\n",
       "      <td>375.850501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-06-01</th>\n",
       "      <td>435.0</td>\n",
       "      <td>72.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>44.939833</td>\n",
       "      <td>417.724971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-07-01</th>\n",
       "      <td>491.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>-16.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>-12.982495</td>\n",
       "      <td>463.833534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-08-01</th>\n",
       "      <td>505.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>-42.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>-32.097255</td>\n",
       "      <td>446.822475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-09-01</th>\n",
       "      <td>404.0</td>\n",
       "      <td>-101.0</td>\n",
       "      <td>-115.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>44.850912</td>\n",
       "      <td>410.676742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-10-01</th>\n",
       "      <td>359.0</td>\n",
       "      <td>-45.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>-12.621965</td>\n",
       "      <td>372.878705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-11-01</th>\n",
       "      <td>310.0</td>\n",
       "      <td>-49.0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>-32.366464</td>\n",
       "      <td>336.494520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-12-01</th>\n",
       "      <td>337.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>44.758257</td>\n",
       "      <td>374.096759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-01-01</th>\n",
       "      <td>360.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>-12.260914</td>\n",
       "      <td>379.494692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-02-01</th>\n",
       "      <td>342.0</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>-41.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>-32.633359</td>\n",
       "      <td>372.138749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-03-01</th>\n",
       "      <td>406.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>44.662918</td>\n",
       "      <td>402.935511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-04-01</th>\n",
       "      <td>396.0</td>\n",
       "      <td>-10.0</td>\n",
       "      <td>-74.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>-11.898998</td>\n",
       "      <td>402.099193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-05-01</th>\n",
       "      <td>420.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>-32.898197</td>\n",
       "      <td>402.587162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-06-01</th>\n",
       "      <td>472.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>44.564566</td>\n",
       "      <td>444.250899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-07-01</th>\n",
       "      <td>548.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>-11.536309</td>\n",
       "      <td>490.127892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-08-01</th>\n",
       "      <td>559.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-65.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>-33.160843</td>\n",
       "      <td>472.793939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-09-01</th>\n",
       "      <td>463.0</td>\n",
       "      <td>-96.0</td>\n",
       "      <td>-107.0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>44.463308</td>\n",
       "      <td>436.359200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-10-01</th>\n",
       "      <td>407.0</td>\n",
       "      <td>-56.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>-11.172867</td>\n",
       "      <td>398.236099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-11-01</th>\n",
       "      <td>362.0</td>\n",
       "      <td>-45.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>-33.421325</td>\n",
       "      <td>361.504613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-12-01</th>\n",
       "      <td>405.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>44.359124</td>\n",
       "      <td>398.923687</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-01-01</th>\n",
       "      <td>417.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>-31.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>-10.808691</td>\n",
       "      <td>403.997715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-02-01</th>\n",
       "      <td>391.0</td>\n",
       "      <td>-26.0</td>\n",
       "      <td>-38.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>-33.679611</td>\n",
       "      <td>396.388914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-03-01</th>\n",
       "      <td>419.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>44.252026</td>\n",
       "      <td>426.917195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-04-01</th>\n",
       "      <td>461.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>65.0</td>\n",
       "      <td>-10.443809</td>\n",
       "      <td>425.799160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-05-01</th>\n",
       "      <td>472.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-31.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>-33.935687</td>\n",
       "      <td>426.039370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-06-01</th>\n",
       "      <td>535.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>44.142021</td>\n",
       "      <td>467.421574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-07-01</th>\n",
       "      <td>622.0</td>\n",
       "      <td>87.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>74.0</td>\n",
       "      <td>-10.078242</td>\n",
       "      <td>513.024457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-08-01</th>\n",
       "      <td>606.0</td>\n",
       "      <td>-16.0</td>\n",
       "      <td>-103.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>-34.189537</td>\n",
       "      <td>495.451019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-09-01</th>\n",
       "      <td>508.0</td>\n",
       "      <td>-98.0</td>\n",
       "      <td>-82.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>44.029116</td>\n",
       "      <td>458.767728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-10-01</th>\n",
       "      <td>461.0</td>\n",
       "      <td>-47.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>-9.712016</td>\n",
       "      <td>420.413021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-11-01</th>\n",
       "      <td>390.0</td>\n",
       "      <td>-71.0</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>-34.441143</td>\n",
       "      <td>383.458594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-12-01</th>\n",
       "      <td>432.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>113.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>43.913318</td>\n",
       "      <td>420.609218</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Thousands of Passengers  Passengers First Difference  \\\n",
       "Month                                                              \n",
       "1956-01-01                    284.0                          6.0   \n",
       "1956-02-01                    277.0                         -7.0   \n",
       "1956-03-01                    317.0                         40.0   \n",
       "1956-04-01                    313.0                         -4.0   \n",
       "1956-05-01                    318.0                          5.0   \n",
       "1956-06-01                    374.0                         56.0   \n",
       "1956-07-01                    413.0                         39.0   \n",
       "1956-08-01                    405.0                         -8.0   \n",
       "1956-09-01                    355.0                        -50.0   \n",
       "1956-10-01                    306.0                        -49.0   \n",
       "1956-11-01                    271.0                        -35.0   \n",
       "1956-12-01                    306.0                         35.0   \n",
       "1957-01-01                    315.0                          9.0   \n",
       "1957-02-01                    301.0                        -14.0   \n",
       "1957-03-01                    356.0                         55.0   \n",
       "1957-04-01                    348.0                         -8.0   \n",
       "1957-05-01                    355.0                          7.0   \n",
       "1957-06-01                    422.0                         67.0   \n",
       "1957-07-01                    465.0                         43.0   \n",
       "1957-08-01                    467.0                          2.0   \n",
       "1957-09-01                    404.0                        -63.0   \n",
       "1957-10-01                    347.0                        -57.0   \n",
       "1957-11-01                    305.0                        -42.0   \n",
       "1957-12-01                    336.0                         31.0   \n",
       "1958-01-01                    340.0                          4.0   \n",
       "1958-02-01                    318.0                        -22.0   \n",
       "1958-03-01                    362.0                         44.0   \n",
       "1958-04-01                    348.0                        -14.0   \n",
       "1958-05-01                    363.0                         15.0   \n",
       "1958-06-01                    435.0                         72.0   \n",
       "1958-07-01                    491.0                         56.0   \n",
       "1958-08-01                    505.0                         14.0   \n",
       "1958-09-01                    404.0                       -101.0   \n",
       "1958-10-01                    359.0                        -45.0   \n",
       "1958-11-01                    310.0                        -49.0   \n",
       "1958-12-01                    337.0                         27.0   \n",
       "1959-01-01                    360.0                         23.0   \n",
       "1959-02-01                    342.0                        -18.0   \n",
       "1959-03-01                    406.0                         64.0   \n",
       "1959-04-01                    396.0                        -10.0   \n",
       "1959-05-01                    420.0                         24.0   \n",
       "1959-06-01                    472.0                         52.0   \n",
       "1959-07-01                    548.0                         76.0   \n",
       "1959-08-01                    559.0                         11.0   \n",
       "1959-09-01                    463.0                        -96.0   \n",
       "1959-10-01                    407.0                        -56.0   \n",
       "1959-11-01                    362.0                        -45.0   \n",
       "1959-12-01                    405.0                         43.0   \n",
       "1960-01-01                    417.0                         12.0   \n",
       "1960-02-01                    391.0                        -26.0   \n",
       "1960-03-01                    419.0                         28.0   \n",
       "1960-04-01                    461.0                         42.0   \n",
       "1960-05-01                    472.0                         11.0   \n",
       "1960-06-01                    535.0                         63.0   \n",
       "1960-07-01                    622.0                         87.0   \n",
       "1960-08-01                    606.0                        -16.0   \n",
       "1960-09-01                    508.0                        -98.0   \n",
       "1960-10-01                    461.0                        -47.0   \n",
       "1960-11-01                    390.0                        -71.0   \n",
       "1960-12-01                    432.0                         42.0   \n",
       "\n",
       "            Passengers Second Difference  Passengers 12 Difference  \\\n",
       "Month                                                                \n",
       "1956-01-01                         -35.0                      42.0   \n",
       "1956-02-01                         -13.0                      44.0   \n",
       "1956-03-01                          47.0                      50.0   \n",
       "1956-04-01                         -44.0                      44.0   \n",
       "1956-05-01                           9.0                      48.0   \n",
       "1956-06-01                          51.0                      59.0   \n",
       "1956-07-01                         -17.0                      49.0   \n",
       "1956-08-01                         -47.0                      58.0   \n",
       "1956-09-01                         -42.0                      43.0   \n",
       "1956-10-01                           1.0                      32.0   \n",
       "1956-11-01                          14.0                      34.0   \n",
       "1956-12-01                          70.0                      28.0   \n",
       "1957-01-01                         -26.0                      31.0   \n",
       "1957-02-01                         -23.0                      24.0   \n",
       "1957-03-01                          69.0                      39.0   \n",
       "1957-04-01                         -63.0                      35.0   \n",
       "1957-05-01                          15.0                      37.0   \n",
       "1957-06-01                          60.0                      48.0   \n",
       "1957-07-01                         -24.0                      52.0   \n",
       "1957-08-01                         -41.0                      62.0   \n",
       "1957-09-01                         -65.0                      49.0   \n",
       "1957-10-01                           6.0                      41.0   \n",
       "1957-11-01                          15.0                      34.0   \n",
       "1957-12-01                          73.0                      30.0   \n",
       "1958-01-01                         -27.0                      25.0   \n",
       "1958-02-01                         -26.0                      17.0   \n",
       "1958-03-01                          66.0                       6.0   \n",
       "1958-04-01                         -58.0                       0.0   \n",
       "1958-05-01                          29.0                       8.0   \n",
       "1958-06-01                          57.0                      13.0   \n",
       "1958-07-01                         -16.0                      26.0   \n",
       "1958-08-01                         -42.0                      38.0   \n",
       "1958-09-01                        -115.0                       0.0   \n",
       "1958-10-01                          56.0                      12.0   \n",
       "1958-11-01                          -4.0                       5.0   \n",
       "1958-12-01                          76.0                       1.0   \n",
       "1959-01-01                          -4.0                      20.0   \n",
       "1959-02-01                         -41.0                      24.0   \n",
       "1959-03-01                          82.0                      44.0   \n",
       "1959-04-01                         -74.0                      48.0   \n",
       "1959-05-01                          34.0                      57.0   \n",
       "1959-06-01                          28.0                      37.0   \n",
       "1959-07-01                          24.0                      57.0   \n",
       "1959-08-01                         -65.0                      54.0   \n",
       "1959-09-01                        -107.0                      59.0   \n",
       "1959-10-01                          40.0                      48.0   \n",
       "1959-11-01                          11.0                      52.0   \n",
       "1959-12-01                          88.0                      68.0   \n",
       "1960-01-01                         -31.0                      57.0   \n",
       "1960-02-01                         -38.0                      49.0   \n",
       "1960-03-01                          54.0                      13.0   \n",
       "1960-04-01                          14.0                      65.0   \n",
       "1960-05-01                         -31.0                      52.0   \n",
       "1960-06-01                          52.0                      63.0   \n",
       "1960-07-01                          24.0                      74.0   \n",
       "1960-08-01                        -103.0                      47.0   \n",
       "1960-09-01                         -82.0                      45.0   \n",
       "1960-10-01                          51.0                      54.0   \n",
       "1960-11-01                         -24.0                      28.0   \n",
       "1960-12-01                         113.0                      27.0   \n",
       "\n",
       "            Predicted_ARIMA  Predicted_SARIMA  \n",
       "Month                                          \n",
       "1956-01-01       -18.162150               NaN  \n",
       "1956-02-01       -45.477686               NaN  \n",
       "1956-03-01        36.823887               NaN  \n",
       "1956-04-01       -13.751486               NaN  \n",
       "1956-05-01       -24.008603               NaN  \n",
       "1956-06-01        47.695447               NaN  \n",
       "1956-07-01       -17.190004        399.012415  \n",
       "1956-08-01       -31.682662        382.942369  \n",
       "1956-09-01        45.053450        347.541878  \n",
       "1956-10-01       -14.879861        310.733630  \n",
       "1956-11-01       -29.599343        275.541082  \n",
       "1956-12-01        45.461525        313.142988  \n",
       "1957-01-01       -15.359948        319.590512  \n",
       "1957-02-01       -30.599654        312.766913  \n",
       "1957-03-01        45.359258        344.240377  \n",
       "1957-04-01       -14.685594        344.173943  \n",
       "1957-05-01       -30.678062        345.215411  \n",
       "1957-06-01        45.253970        387.676459  \n",
       "1957-07-01       -14.443474        434.322457  \n",
       "1957-08-01       -31.010197        417.510876  \n",
       "1957-09-01        45.198710        381.686456  \n",
       "1957-10-01       -14.048689        344.056058  \n",
       "1957-11-01       -31.275681        307.775441  \n",
       "1957-12-01        45.107187        345.978918  \n",
       "1958-01-01       -13.703068        351.527557  \n",
       "1958-02-01       -31.553004        344.523221  \n",
       "1958-03-01        45.028083        375.622211  \n",
       "1958-04-01       -13.340926        375.020011  \n",
       "1958-05-01       -31.826277        375.850501  \n",
       "1958-06-01        44.939833        417.724971  \n",
       "1958-07-01       -12.982495        463.833534  \n",
       "1958-08-01       -32.097255        446.822475  \n",
       "1958-09-01        44.850912        410.676742  \n",
       "1958-10-01       -12.621965        372.878705  \n",
       "1958-11-01       -32.366464        336.494520  \n",
       "1958-12-01        44.758257        374.096759  \n",
       "1959-01-01       -12.260914        379.494692  \n",
       "1959-02-01       -32.633359        372.138749  \n",
       "1959-03-01        44.662918        402.935511  \n",
       "1959-04-01       -11.898998        402.099193  \n",
       "1959-05-01       -32.898197        402.587162  \n",
       "1959-06-01        44.564566        444.250899  \n",
       "1959-07-01       -11.536309        490.127892  \n",
       "1959-08-01       -33.160843        472.793939  \n",
       "1959-09-01        44.463308        436.359200  \n",
       "1959-10-01       -11.172867        398.236099  \n",
       "1959-11-01       -33.421325        361.504613  \n",
       "1959-12-01        44.359124        398.923687  \n",
       "1960-01-01       -10.808691        403.997715  \n",
       "1960-02-01       -33.679611        396.388914  \n",
       "1960-03-01        44.252026        426.917195  \n",
       "1960-04-01       -10.443809        425.799160  \n",
       "1960-05-01       -33.935687        426.039370  \n",
       "1960-06-01        44.142021        467.421574  \n",
       "1960-07-01       -10.078242        513.024457  \n",
       "1960-08-01       -34.189537        495.451019  \n",
       "1960-09-01        44.029116        458.767728  \n",
       "1960-10-01        -9.712016        420.413021  \n",
       "1960-11-01       -34.441143        383.458594  \n",
       "1960-12-01        43.913318        420.609218  "
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "27efedb7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1956-01-01 00:00:00\n",
      "1960-12-01 00:00:00\n"
     ]
    }
   ],
   "source": [
    "##prediction\n",
    "pred_start_date=test_data.index[0]\n",
    "pred_end_date=test_data.index[-1]\n",
    "print(pred_start_date)\n",
    "print(pred_end_date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "54ab81f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\win10\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:132: FutureWarning: The 'freq' argument in Timestamp is deprecated and will be removed in a future version.\n",
      "  date_key = Timestamp(key, freq=base_index.freq)\n"
     ]
    }
   ],
   "source": [
    "pred=model_Arima_fit.predict(start=pred_start_date,end=pred_end_date)\n",
    "residuals=test_data['Thousands of Passengers']-pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "f84a6a84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1956-01-01   -18.162150\n",
       "1956-02-01   -45.477686\n",
       "1956-03-01    36.823887\n",
       "1956-04-01   -13.751486\n",
       "1956-05-01   -24.008603\n",
       "1956-06-01    47.695447\n",
       "1956-07-01   -17.190004\n",
       "1956-08-01   -31.682662\n",
       "1956-09-01    45.053450\n",
       "1956-10-01   -14.879861\n",
       "1956-11-01   -29.599343\n",
       "1956-12-01    45.461525\n",
       "1957-01-01   -15.359948\n",
       "1957-02-01   -30.599654\n",
       "1957-03-01    45.359258\n",
       "1957-04-01   -14.685594\n",
       "1957-05-01   -30.678062\n",
       "1957-06-01    45.253970\n",
       "1957-07-01   -14.443474\n",
       "1957-08-01   -31.010197\n",
       "1957-09-01    45.198710\n",
       "1957-10-01   -14.048689\n",
       "1957-11-01   -31.275681\n",
       "1957-12-01    45.107187\n",
       "1958-01-01   -13.703068\n",
       "1958-02-01   -31.553004\n",
       "1958-03-01    45.028083\n",
       "1958-04-01   -13.340926\n",
       "1958-05-01   -31.826277\n",
       "1958-06-01    44.939833\n",
       "1958-07-01   -12.982495\n",
       "1958-08-01   -32.097255\n",
       "1958-09-01    44.850912\n",
       "1958-10-01   -12.621965\n",
       "1958-11-01   -32.366464\n",
       "1958-12-01    44.758257\n",
       "1959-01-01   -12.260914\n",
       "1959-02-01   -32.633359\n",
       "1959-03-01    44.662918\n",
       "1959-04-01   -11.898998\n",
       "1959-05-01   -32.898197\n",
       "1959-06-01    44.564566\n",
       "1959-07-01   -11.536309\n",
       "1959-08-01   -33.160843\n",
       "1959-09-01    44.463308\n",
       "1959-10-01   -11.172867\n",
       "1959-11-01   -33.421325\n",
       "1959-12-01    44.359124\n",
       "1960-01-01   -10.808691\n",
       "1960-02-01   -33.679611\n",
       "1960-03-01    44.252026\n",
       "1960-04-01   -10.443809\n",
       "1960-05-01   -33.935687\n",
       "1960-06-01    44.142021\n",
       "1960-07-01   -10.078242\n",
       "1960-08-01   -34.189537\n",
       "1960-09-01    44.029116\n",
       "1960-10-01    -9.712016\n",
       "1960-11-01   -34.441143\n",
       "1960-12-01    43.913318\n",
       "Freq: MS, dtype: float64"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "c057759e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Month\n",
       "1956-01-01    302.162150\n",
       "1956-02-01    322.477686\n",
       "1956-03-01    280.176113\n",
       "1956-04-01    326.751486\n",
       "1956-05-01    342.008603\n",
       "1956-06-01    326.304553\n",
       "1956-07-01    430.190004\n",
       "1956-08-01    436.682662\n",
       "1956-09-01    309.946550\n",
       "1956-10-01    320.879861\n",
       "1956-11-01    300.599343\n",
       "1956-12-01    260.538475\n",
       "1957-01-01    330.359948\n",
       "1957-02-01    331.599654\n",
       "1957-03-01    310.640742\n",
       "1957-04-01    362.685594\n",
       "1957-05-01    385.678062\n",
       "1957-06-01    376.746030\n",
       "1957-07-01    479.443474\n",
       "1957-08-01    498.010197\n",
       "1957-09-01    358.801290\n",
       "1957-10-01    361.048689\n",
       "1957-11-01    336.275681\n",
       "1957-12-01    290.892813\n",
       "1958-01-01    353.703068\n",
       "1958-02-01    349.553004\n",
       "1958-03-01    316.971917\n",
       "1958-04-01    361.340926\n",
       "1958-05-01    394.826277\n",
       "1958-06-01    390.060167\n",
       "1958-07-01    503.982495\n",
       "1958-08-01    537.097255\n",
       "1958-09-01    359.149088\n",
       "1958-10-01    371.621965\n",
       "1958-11-01    342.366464\n",
       "1958-12-01    292.241743\n",
       "1959-01-01    372.260914\n",
       "1959-02-01    374.633359\n",
       "1959-03-01    361.337082\n",
       "1959-04-01    407.898998\n",
       "1959-05-01    452.898197\n",
       "1959-06-01    427.435434\n",
       "1959-07-01    559.536309\n",
       "1959-08-01    592.160843\n",
       "1959-09-01    418.536692\n",
       "1959-10-01    418.172867\n",
       "1959-11-01    395.421325\n",
       "1959-12-01    360.640876\n",
       "1960-01-01    427.808691\n",
       "1960-02-01    424.679611\n",
       "1960-03-01    374.747974\n",
       "1960-04-01    471.443809\n",
       "1960-05-01    505.935687\n",
       "1960-06-01    490.857979\n",
       "1960-07-01    632.078242\n",
       "1960-08-01    640.189537\n",
       "1960-09-01    463.970884\n",
       "1960-10-01    470.712016\n",
       "1960-11-01    424.441143\n",
       "1960-12-01    388.086682\n",
       "dtype: float64"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "1b760c60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_Arima_fit.resid.plot(kind='kde')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "cf4e08a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\win10\\AppData\\Local\\Temp/ipykernel_32852/95659616.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  test_data['Predicted_ARIMA']=pred\n"
     ]
    }
   ],
   "source": [
    "test_data['Predicted_ARIMA']=pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "218ef4d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Month'>"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_data[['Thousands of Passengers','Predicted_ARIMA']].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "aa962999",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf12 = plot_acf(df_airline[\"Passengers 12 Difference\"].dropna())\n",
    "pacf12 = plot_pacf(df_airline[\"Passengers 12 Difference\"].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "86230e68",
   "metadata": {},
   "outputs": [],
   "source": [
    "## create a SARIMA model\n",
    "from statsmodels.tsa.statespace.sarimax import SARIMAX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "1da12cb6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\win10\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  warnings.warn('No frequency information was'\n",
      "C:\\Users\\win10\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  warnings.warn('No frequency information was'\n"
     ]
    }
   ],
   "source": [
    "model_SARIMA=SARIMAX(train_data['Thousands of Passengers'],order=(3,0,5),seasonal_order=(0,1,0,12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "19dcd73a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\win10\\anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n"
     ]
    }
   ],
   "source": [
    "model_SARIMA_fit=model_SARIMA.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "1864abb5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>SARIMAX Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>Thousands of Passengers</td>     <th>  No. Observations:  </th>    <td>84</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>SARIMAX(3, 0, 5)x(1, 1, [1], 12)</td> <th>  Log Likelihood     </th> <td>-263.918</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>                    <td>Sun, 27 Feb 2022</td>         <th>  AIC                </th>  <td>549.836</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                        <td>20:07:02</td>             <th>  BIC                </th>  <td>574.880</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>                     <td>01-01-1949</td>            <th>  HQIC               </th>  <td>559.806</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                           <td>- 12-01-1955</td>           <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>                <td>opg</td>               <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th>    <td>    0.5532</td> <td>    3.048</td> <td>    0.181</td> <td> 0.856</td> <td>   -5.421</td> <td>    6.527</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2</th>    <td>    0.8499</td> <td>    0.367</td> <td>    2.318</td> <td> 0.020</td> <td>    0.131</td> <td>    1.568</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3</th>    <td>   -0.4143</td> <td>    2.779</td> <td>   -0.149</td> <td> 0.881</td> <td>   -5.861</td> <td>    5.032</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1</th>    <td>    0.2055</td> <td>    2.967</td> <td>    0.069</td> <td> 0.945</td> <td>   -5.609</td> <td>    6.020</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2</th>    <td>   -0.5098</td> <td>    2.189</td> <td>   -0.233</td> <td> 0.816</td> <td>   -4.800</td> <td>    3.780</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3</th>    <td>   -0.0916</td> <td>    0.642</td> <td>   -0.143</td> <td> 0.887</td> <td>   -1.350</td> <td>    1.167</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L4</th>    <td>   -0.1883</td> <td>    0.479</td> <td>   -0.393</td> <td> 0.694</td> <td>   -1.127</td> <td>    0.750</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L5</th>    <td>    0.1676</td> <td>    0.826</td> <td>    0.203</td> <td> 0.839</td> <td>   -1.451</td> <td>    1.786</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.S.L12</th> <td>   -0.3096</td> <td>    0.868</td> <td>   -0.357</td> <td> 0.721</td> <td>   -2.011</td> <td>    1.392</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.S.L12</th> <td>    0.1029</td> <td>    0.954</td> <td>    0.108</td> <td> 0.914</td> <td>   -1.766</td> <td>    1.972</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th>   <td>   83.8549</td> <td>   28.404</td> <td>    2.952</td> <td> 0.003</td> <td>   28.184</td> <td>  139.526</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Ljung-Box (L1) (Q):</th>     <td>0.01</td> <th>  Jarque-Bera (JB):  </th> <td>1.94</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Q):</th>                <td>0.93</td> <th>  Prob(JB):          </th> <td>0.38</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Heteroskedasticity (H):</th> <td>2.41</td> <th>  Skew:              </th> <td>0.40</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(H) (two-sided):</th>    <td>0.04</td> <th>  Kurtosis:          </th> <td>2.94</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using the outer product of gradients (complex-step)."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                      SARIMAX Results                                       \n",
       "============================================================================================\n",
       "Dep. Variable:              Thousands of Passengers   No. Observations:                   84\n",
       "Model:             SARIMAX(3, 0, 5)x(1, 1, [1], 12)   Log Likelihood                -263.918\n",
       "Date:                              Sun, 27 Feb 2022   AIC                            549.836\n",
       "Time:                                      20:07:02   BIC                            574.880\n",
       "Sample:                                  01-01-1949   HQIC                           559.806\n",
       "                                       - 12-01-1955                                         \n",
       "Covariance Type:                                opg                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "ar.L1          0.5532      3.048      0.181      0.856      -5.421       6.527\n",
       "ar.L2          0.8499      0.367      2.318      0.020       0.131       1.568\n",
       "ar.L3         -0.4143      2.779     -0.149      0.881      -5.861       5.032\n",
       "ma.L1          0.2055      2.967      0.069      0.945      -5.609       6.020\n",
       "ma.L2         -0.5098      2.189     -0.233      0.816      -4.800       3.780\n",
       "ma.L3         -0.0916      0.642     -0.143      0.887      -1.350       1.167\n",
       "ma.L4         -0.1883      0.479     -0.393      0.694      -1.127       0.750\n",
       "ma.L5          0.1676      0.826      0.203      0.839      -1.451       1.786\n",
       "ar.S.L12      -0.3096      0.868     -0.357      0.721      -2.011       1.392\n",
       "ma.S.L12       0.1029      0.954      0.108      0.914      -1.766       1.972\n",
       "sigma2        83.8549     28.404      2.952      0.003      28.184     139.526\n",
       "===================================================================================\n",
       "Ljung-Box (L1) (Q):                   0.01   Jarque-Bera (JB):                 1.94\n",
       "Prob(Q):                              0.93   Prob(JB):                         0.38\n",
       "Heteroskedasticity (H):               2.41   Skew:                             0.40\n",
       "Prob(H) (two-sided):                  0.04   Kurtosis:                         2.94\n",
       "===================================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
       "\"\"\""
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_SARIMA_fit.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "7b8fc9aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "      <th>Passengers First Difference</th>\n",
       "      <th>Passengers Second Difference</th>\n",
       "      <th>Passengers 12 Difference</th>\n",
       "      <th>Predicted_ARIMA</th>\n",
       "      <th>Predicted_SARIMA</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1960-08-01</th>\n",
       "      <td>606.0</td>\n",
       "      <td>-16.0</td>\n",
       "      <td>-103.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>0.0574</td>\n",
       "      <td>2559.875517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-09-01</th>\n",
       "      <td>508.0</td>\n",
       "      <td>-98.0</td>\n",
       "      <td>-82.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>0.0574</td>\n",
       "      <td>2583.976044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-10-01</th>\n",
       "      <td>461.0</td>\n",
       "      <td>-47.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.0574</td>\n",
       "      <td>2608.365234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-11-01</th>\n",
       "      <td>390.0</td>\n",
       "      <td>-71.0</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0.0574</td>\n",
       "      <td>2633.890859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-12-01</th>\n",
       "      <td>432.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>113.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0.0574</td>\n",
       "      <td>2726.249847</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Thousands of Passengers  Passengers First Difference  \\\n",
       "Month                                                              \n",
       "1960-08-01                    606.0                        -16.0   \n",
       "1960-09-01                    508.0                        -98.0   \n",
       "1960-10-01                    461.0                        -47.0   \n",
       "1960-11-01                    390.0                        -71.0   \n",
       "1960-12-01                    432.0                         42.0   \n",
       "\n",
       "            Passengers Second Difference  Passengers 12 Difference  \\\n",
       "Month                                                                \n",
       "1960-08-01                        -103.0                      47.0   \n",
       "1960-09-01                         -82.0                      45.0   \n",
       "1960-10-01                          51.0                      54.0   \n",
       "1960-11-01                         -24.0                      28.0   \n",
       "1960-12-01                         113.0                      27.0   \n",
       "\n",
       "            Predicted_ARIMA  Predicted_SARIMA  \n",
       "Month                                          \n",
       "1960-08-01           0.0574       2559.875517  \n",
       "1960-09-01           0.0574       2583.976044  \n",
       "1960-10-01           0.0574       2608.365234  \n",
       "1960-11-01           0.0574       2633.890859  \n",
       "1960-12-01           0.0574       2726.249847  "
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "1eee263a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1956-01-01 00:00:00\n",
      "1960-12-01 00:00:00\n"
     ]
    }
   ],
   "source": [
    "##prediction\n",
    "pred_start_date=test_data.index[0]\n",
    "pred_end_date=test_data.index[-1]\n",
    "print(pred_start_date)\n",
    "print(pred_end_date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "1f412af2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\win10\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:132: FutureWarning: The 'freq' argument in Timestamp is deprecated and will be removed in a future version.\n",
      "  date_key = Timestamp(key, freq=base_index.freq)\n"
     ]
    }
   ],
   "source": [
    "pred_Sarima=model_SARIMA_fit.predict(start=datetime(1956,6,6),end=datetime(1960,12,1))\n",
    "residuals=test_data['Thousands of Passengers']-pred_Sarima"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "7d168cc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Month'>"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_SARIMA_fit.resid.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "6e9bf0c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_SARIMA_fit.resid.plot(kind='kde')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "881e896f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\win10\\AppData\\Local\\Temp/ipykernel_32852/1367177785.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  test_data['Predicted_SARIMA']=pred_Sarima\n"
     ]
    }
   ],
   "source": [
    "test_data['Predicted_SARIMA']=pred_Sarima"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "bf0c3078",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Thousands of Passengers</th>\n",
       "      <th>Passengers First Difference</th>\n",
       "      <th>Passengers Second Difference</th>\n",
       "      <th>Passengers 12 Difference</th>\n",
       "      <th>Predicted_ARIMA</th>\n",
       "      <th>Predicted_SARIMA</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1956-01-01</th>\n",
       "      <td>284.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>-35.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>2.909341</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-02-01</th>\n",
       "      <td>277.0</td>\n",
       "      <td>-7.0</td>\n",
       "      <td>-13.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>-1.874060</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-03-01</th>\n",
       "      <td>317.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>-27.004647</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-04-01</th>\n",
       "      <td>313.0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>-44.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>-17.471389</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-05-01</th>\n",
       "      <td>318.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>-31.452655</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-06-01</th>\n",
       "      <td>374.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>26.843422</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-07-01</th>\n",
       "      <td>413.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>-17.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>26.892167</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-08-01</th>\n",
       "      <td>405.0</td>\n",
       "      <td>-8.0</td>\n",
       "      <td>-47.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>-20.461356</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-09-01</th>\n",
       "      <td>355.0</td>\n",
       "      <td>-50.0</td>\n",
       "      <td>-42.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>28.590874</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-10-01</th>\n",
       "      <td>306.0</td>\n",
       "      <td>-49.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>-24.715282</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-11-01</th>\n",
       "      <td>271.0</td>\n",
       "      <td>-35.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1956-12-01</th>\n",
       "      <td>306.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-01-01</th>\n",
       "      <td>315.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>-26.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-02-01</th>\n",
       "      <td>301.0</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>-23.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-03-01</th>\n",
       "      <td>356.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-04-01</th>\n",
       "      <td>348.0</td>\n",
       "      <td>-8.0</td>\n",
       "      <td>-63.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-05-01</th>\n",
       "      <td>355.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-06-01</th>\n",
       "      <td>422.0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-07-01</th>\n",
       "      <td>465.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-08-01</th>\n",
       "      <td>467.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>-41.0</td>\n",
       "      <td>62.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-09-01</th>\n",
       "      <td>404.0</td>\n",
       "      <td>-63.0</td>\n",
       "      <td>-65.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-10-01</th>\n",
       "      <td>347.0</td>\n",
       "      <td>-57.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>41.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-11-01</th>\n",
       "      <td>305.0</td>\n",
       "      <td>-42.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1957-12-01</th>\n",
       "      <td>336.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>73.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-01-01</th>\n",
       "      <td>340.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-27.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-02-01</th>\n",
       "      <td>318.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>-26.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-03-01</th>\n",
       "      <td>362.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-04-01</th>\n",
       "      <td>348.0</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>-58.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-05-01</th>\n",
       "      <td>363.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-06-01</th>\n",
       "      <td>435.0</td>\n",
       "      <td>72.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-07-01</th>\n",
       "      <td>491.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>-16.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-08-01</th>\n",
       "      <td>505.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>-42.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-09-01</th>\n",
       "      <td>404.0</td>\n",
       "      <td>-101.0</td>\n",
       "      <td>-115.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-10-01</th>\n",
       "      <td>359.0</td>\n",
       "      <td>-45.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-11-01</th>\n",
       "      <td>310.0</td>\n",
       "      <td>-49.0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1958-12-01</th>\n",
       "      <td>337.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-01-01</th>\n",
       "      <td>360.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-02-01</th>\n",
       "      <td>342.0</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>-41.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-03-01</th>\n",
       "      <td>406.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-04-01</th>\n",
       "      <td>396.0</td>\n",
       "      <td>-10.0</td>\n",
       "      <td>-74.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-05-01</th>\n",
       "      <td>420.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-06-01</th>\n",
       "      <td>472.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-07-01</th>\n",
       "      <td>548.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-08-01</th>\n",
       "      <td>559.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-65.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-09-01</th>\n",
       "      <td>463.0</td>\n",
       "      <td>-96.0</td>\n",
       "      <td>-107.0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-10-01</th>\n",
       "      <td>407.0</td>\n",
       "      <td>-56.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-11-01</th>\n",
       "      <td>362.0</td>\n",
       "      <td>-45.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959-12-01</th>\n",
       "      <td>405.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-01-01</th>\n",
       "      <td>417.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>-31.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-02-01</th>\n",
       "      <td>391.0</td>\n",
       "      <td>-26.0</td>\n",
       "      <td>-38.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-03-01</th>\n",
       "      <td>419.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-04-01</th>\n",
       "      <td>461.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>65.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-05-01</th>\n",
       "      <td>472.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-31.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-06-01</th>\n",
       "      <td>535.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-07-01</th>\n",
       "      <td>622.0</td>\n",
       "      <td>87.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>74.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>2512.809187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-08-01</th>\n",
       "      <td>606.0</td>\n",
       "      <td>-16.0</td>\n",
       "      <td>-103.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>2559.875517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-09-01</th>\n",
       "      <td>508.0</td>\n",
       "      <td>-98.0</td>\n",
       "      <td>-82.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>2583.976044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-10-01</th>\n",
       "      <td>461.0</td>\n",
       "      <td>-47.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>2608.365234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-11-01</th>\n",
       "      <td>390.0</td>\n",
       "      <td>-71.0</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>2633.890859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1960-12-01</th>\n",
       "      <td>432.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>113.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0.057400</td>\n",
       "      <td>2726.249847</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Thousands of Passengers  Passengers First Difference  \\\n",
       "Month                                                              \n",
       "1956-01-01                    284.0                          6.0   \n",
       "1956-02-01                    277.0                         -7.0   \n",
       "1956-03-01                    317.0                         40.0   \n",
       "1956-04-01                    313.0                         -4.0   \n",
       "1956-05-01                    318.0                          5.0   \n",
       "1956-06-01                    374.0                         56.0   \n",
       "1956-07-01                    413.0                         39.0   \n",
       "1956-08-01                    405.0                         -8.0   \n",
       "1956-09-01                    355.0                        -50.0   \n",
       "1956-10-01                    306.0                        -49.0   \n",
       "1956-11-01                    271.0                        -35.0   \n",
       "1956-12-01                    306.0                         35.0   \n",
       "1957-01-01                    315.0                          9.0   \n",
       "1957-02-01                    301.0                        -14.0   \n",
       "1957-03-01                    356.0                         55.0   \n",
       "1957-04-01                    348.0                         -8.0   \n",
       "1957-05-01                    355.0                          7.0   \n",
       "1957-06-01                    422.0                         67.0   \n",
       "1957-07-01                    465.0                         43.0   \n",
       "1957-08-01                    467.0                          2.0   \n",
       "1957-09-01                    404.0                        -63.0   \n",
       "1957-10-01                    347.0                        -57.0   \n",
       "1957-11-01                    305.0                        -42.0   \n",
       "1957-12-01                    336.0                         31.0   \n",
       "1958-01-01                    340.0                          4.0   \n",
       "1958-02-01                    318.0                        -22.0   \n",
       "1958-03-01                    362.0                         44.0   \n",
       "1958-04-01                    348.0                        -14.0   \n",
       "1958-05-01                    363.0                         15.0   \n",
       "1958-06-01                    435.0                         72.0   \n",
       "1958-07-01                    491.0                         56.0   \n",
       "1958-08-01                    505.0                         14.0   \n",
       "1958-09-01                    404.0                       -101.0   \n",
       "1958-10-01                    359.0                        -45.0   \n",
       "1958-11-01                    310.0                        -49.0   \n",
       "1958-12-01                    337.0                         27.0   \n",
       "1959-01-01                    360.0                         23.0   \n",
       "1959-02-01                    342.0                        -18.0   \n",
       "1959-03-01                    406.0                         64.0   \n",
       "1959-04-01                    396.0                        -10.0   \n",
       "1959-05-01                    420.0                         24.0   \n",
       "1959-06-01                    472.0                         52.0   \n",
       "1959-07-01                    548.0                         76.0   \n",
       "1959-08-01                    559.0                         11.0   \n",
       "1959-09-01                    463.0                        -96.0   \n",
       "1959-10-01                    407.0                        -56.0   \n",
       "1959-11-01                    362.0                        -45.0   \n",
       "1959-12-01                    405.0                         43.0   \n",
       "1960-01-01                    417.0                         12.0   \n",
       "1960-02-01                    391.0                        -26.0   \n",
       "1960-03-01                    419.0                         28.0   \n",
       "1960-04-01                    461.0                         42.0   \n",
       "1960-05-01                    472.0                         11.0   \n",
       "1960-06-01                    535.0                         63.0   \n",
       "1960-07-01                    622.0                         87.0   \n",
       "1960-08-01                    606.0                        -16.0   \n",
       "1960-09-01                    508.0                        -98.0   \n",
       "1960-10-01                    461.0                        -47.0   \n",
       "1960-11-01                    390.0                        -71.0   \n",
       "1960-12-01                    432.0                         42.0   \n",
       "\n",
       "            Passengers Second Difference  Passengers 12 Difference  \\\n",
       "Month                                                                \n",
       "1956-01-01                         -35.0                      42.0   \n",
       "1956-02-01                         -13.0                      44.0   \n",
       "1956-03-01                          47.0                      50.0   \n",
       "1956-04-01                         -44.0                      44.0   \n",
       "1956-05-01                           9.0                      48.0   \n",
       "1956-06-01                          51.0                      59.0   \n",
       "1956-07-01                         -17.0                      49.0   \n",
       "1956-08-01                         -47.0                      58.0   \n",
       "1956-09-01                         -42.0                      43.0   \n",
       "1956-10-01                           1.0                      32.0   \n",
       "1956-11-01                          14.0                      34.0   \n",
       "1956-12-01                          70.0                      28.0   \n",
       "1957-01-01                         -26.0                      31.0   \n",
       "1957-02-01                         -23.0                      24.0   \n",
       "1957-03-01                          69.0                      39.0   \n",
       "1957-04-01                         -63.0                      35.0   \n",
       "1957-05-01                          15.0                      37.0   \n",
       "1957-06-01                          60.0                      48.0   \n",
       "1957-07-01                         -24.0                      52.0   \n",
       "1957-08-01                         -41.0                      62.0   \n",
       "1957-09-01                         -65.0                      49.0   \n",
       "1957-10-01                           6.0                      41.0   \n",
       "1957-11-01                          15.0                      34.0   \n",
       "1957-12-01                          73.0                      30.0   \n",
       "1958-01-01                         -27.0                      25.0   \n",
       "1958-02-01                         -26.0                      17.0   \n",
       "1958-03-01                          66.0                       6.0   \n",
       "1958-04-01                         -58.0                       0.0   \n",
       "1958-05-01                          29.0                       8.0   \n",
       "1958-06-01                          57.0                      13.0   \n",
       "1958-07-01                         -16.0                      26.0   \n",
       "1958-08-01                         -42.0                      38.0   \n",
       "1958-09-01                        -115.0                       0.0   \n",
       "1958-10-01                          56.0                      12.0   \n",
       "1958-11-01                          -4.0                       5.0   \n",
       "1958-12-01                          76.0                       1.0   \n",
       "1959-01-01                          -4.0                      20.0   \n",
       "1959-02-01                         -41.0                      24.0   \n",
       "1959-03-01                          82.0                      44.0   \n",
       "1959-04-01                         -74.0                      48.0   \n",
       "1959-05-01                          34.0                      57.0   \n",
       "1959-06-01                          28.0                      37.0   \n",
       "1959-07-01                          24.0                      57.0   \n",
       "1959-08-01                         -65.0                      54.0   \n",
       "1959-09-01                        -107.0                      59.0   \n",
       "1959-10-01                          40.0                      48.0   \n",
       "1959-11-01                          11.0                      52.0   \n",
       "1959-12-01                          88.0                      68.0   \n",
       "1960-01-01                         -31.0                      57.0   \n",
       "1960-02-01                         -38.0                      49.0   \n",
       "1960-03-01                          54.0                      13.0   \n",
       "1960-04-01                          14.0                      65.0   \n",
       "1960-05-01                         -31.0                      52.0   \n",
       "1960-06-01                          52.0                      63.0   \n",
       "1960-07-01                          24.0                      74.0   \n",
       "1960-08-01                        -103.0                      47.0   \n",
       "1960-09-01                         -82.0                      45.0   \n",
       "1960-10-01                          51.0                      54.0   \n",
       "1960-11-01                         -24.0                      28.0   \n",
       "1960-12-01                         113.0                      27.0   \n",
       "\n",
       "            Predicted_ARIMA  Predicted_SARIMA  \n",
       "Month                                          \n",
       "1956-01-01         2.909341               NaN  \n",
       "1956-02-01        -1.874060               NaN  \n",
       "1956-03-01       -27.004647               NaN  \n",
       "1956-04-01       -17.471389               NaN  \n",
       "1956-05-01       -31.452655               NaN  \n",
       "1956-06-01        26.843422               NaN  \n",
       "1956-07-01        26.892167               NaN  \n",
       "1956-08-01       -20.461356               NaN  \n",
       "1956-09-01        28.590874               NaN  \n",
       "1956-10-01       -24.715282               NaN  \n",
       "1956-11-01         0.057400               NaN  \n",
       "1956-12-01         0.057400               NaN  \n",
       "1957-01-01         0.057400               NaN  \n",
       "1957-02-01         0.057400               NaN  \n",
       "1957-03-01         0.057400               NaN  \n",
       "1957-04-01         0.057400               NaN  \n",
       "1957-05-01         0.057400               NaN  \n",
       "1957-06-01         0.057400               NaN  \n",
       "1957-07-01         0.057400               NaN  \n",
       "1957-08-01         0.057400               NaN  \n",
       "1957-09-01         0.057400               NaN  \n",
       "1957-10-01         0.057400               NaN  \n",
       "1957-11-01         0.057400               NaN  \n",
       "1957-12-01         0.057400               NaN  \n",
       "1958-01-01         0.057400               NaN  \n",
       "1958-02-01         0.057400               NaN  \n",
       "1958-03-01         0.057400               NaN  \n",
       "1958-04-01         0.057400               NaN  \n",
       "1958-05-01         0.057400               NaN  \n",
       "1958-06-01         0.057400               NaN  \n",
       "1958-07-01         0.057400               NaN  \n",
       "1958-08-01         0.057400               NaN  \n",
       "1958-09-01         0.057400               NaN  \n",
       "1958-10-01         0.057400               NaN  \n",
       "1958-11-01         0.057400               NaN  \n",
       "1958-12-01         0.057400               NaN  \n",
       "1959-01-01         0.057400               NaN  \n",
       "1959-02-01         0.057400               NaN  \n",
       "1959-03-01         0.057400               NaN  \n",
       "1959-04-01         0.057400               NaN  \n",
       "1959-05-01         0.057400               NaN  \n",
       "1959-06-01         0.057400               NaN  \n",
       "1959-07-01         0.057400               NaN  \n",
       "1959-08-01         0.057400               NaN  \n",
       "1959-09-01         0.057400               NaN  \n",
       "1959-10-01         0.057400               NaN  \n",
       "1959-11-01         0.057400               NaN  \n",
       "1959-12-01         0.057400               NaN  \n",
       "1960-01-01         0.057400               NaN  \n",
       "1960-02-01         0.057400               NaN  \n",
       "1960-03-01         0.057400               NaN  \n",
       "1960-04-01         0.057400               NaN  \n",
       "1960-05-01         0.057400               NaN  \n",
       "1960-06-01         0.057400               NaN  \n",
       "1960-07-01         0.057400       2512.809187  \n",
       "1960-08-01         0.057400       2559.875517  \n",
       "1960-09-01         0.057400       2583.976044  \n",
       "1960-10-01         0.057400       2608.365234  \n",
       "1960-11-01         0.057400       2633.890859  \n",
       "1960-12-01         0.057400       2726.249847  "
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "c4ed646d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Month'>"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_data[['Thousands of Passengers','Predicted_SARIMA','Predicted_ARIMA']].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "493565dc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}