Ocean Two Time series Gaussian Process Regression.ipynb

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    "## Time Series Forecasting using Gaussian Process Regression\n",
    "\n",
    "The following analysis were largely borrowed from [this tutorial](https://docs.pymc.io/notebooks/GP-MaunaLoa.html).\n",
    "\n",
    "Gaussian processes, timeseries analysis, Bayesian modelling"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pymc3 as pm\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import theano.tensor as tt\n",
    "\n",
    "from bokeh.plotting import figure, show\n",
    "from bokeh.models import BoxAnnotation, Span, Label, Legend\n",
    "from bokeh.io import output_notebook\n",
    "from bokeh.palettes import brewer\n",
    "output_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preprocess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_excel('concat_raw_o2.xlsx')\n",
    "df[['DATE', 'DAY_OF_WEEK']] = df['DATE'].str.split(' ', n=1, expand=True)\n",
    "df['DATE'] = pd.to_datetime(df['DATE'])\n",
    "df = df.sort_values('DATE')\n",
    "df.set_index('DATE', inplace=True)\n",
    "df = df['2016-01-01':'2019-08-04']\n",
    "df = df.loc[df['IND REV'] >=0]\n",
    "df = df.loc[~df.index.duplicated(keep='first')]\n",
    "data_columns = ['OCC %', 'REVENUE', 'AVE RATE']\n",
    "# Resample to monthly frequency, aggregating with mean\n",
    "monthly_mean = df[data_columns].resample('M').mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dates_to_idx(timelist):\n",
    "    reference_time = pd.to_datetime('2016-01-31')\n",
    "    t = (timelist - reference_time) / pd.Timedelta(1, \"Y\")\n",
    "    return np.asarray(t)\n",
    "\n",
    "t = dates_to_idx(monthly_mean.index)\n",
    "\n",
    "# normalize CO2 levels\n",
    "y = monthly_mean[\"REVENUE\"].values\n",
    "first_rev = y[0]\n",
    "std_rev = np.std(y)\n",
    "y_n = (y - first_rev) / std_rev\n",
    "\n",
    "monthly_mean = monthly_mean.assign(t = t)\n",
    "monthly_mean = monthly_mean.assign(y_n = y_n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split into training and test set\n",
    "sep_idx = monthly_mean.index.searchsorted(pd.to_datetime(\"2019-01-01\"))\n",
    "data_early = monthly_mean.iloc[:sep_idx+1, :]\n",
    "data_later = monthly_mean.iloc[sep_idx:, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"e9626bdd-7362-4755-a07c-f125ff10e492\" data-root-id=\"1204\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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Set\",\"x\":100,\"x_units\":\"screen\",\"y\":30,\"y_units\":\"screen\"},\"id\":\"1250\",\"type\":\"Label\"},{\"attributes\":{},\"id\":\"1230\",\"type\":\"HelpTool\"},{\"attributes\":{\"months\":[0,2,4,6,8,10]},\"id\":\"1287\",\"type\":\"MonthsTicker\"},{\"attributes\":{\"axis_label\":\"Revenue\",\"formatter\":{\"id\":\"1278\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1221\",\"type\":\"BasicTicker\"}},\"id\":\"1220\",\"type\":\"LinearAxis\"},{\"attributes\":{\"text\":\"Monthly Average Revenue of Ocean Two\"},\"id\":\"1205\",\"type\":\"Title\"},{\"attributes\":{\"callback\":null},\"id\":\"1207\",\"type\":\"DataRange1d\"},{\"attributes\":{\"source\":{\"id\":\"1240\",\"type\":\"ColumnDataSource\"}},\"id\":\"1244\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1276\",\"type\":\"DatetimeTickFormatter\"},{\"attributes\":{\"months\":[0,4,8]},\"id\":\"1288\",\"type\":\"MonthsTicker\"},{\"attributes\":{\"line_alpha\":0.5,\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1241\",\"type\":\"Line\"},{\"attributes\":{\"overlay\":{\"id\":\"1295\",\"type\":\"BoxAnnotation\"}},\"id\":\"1227\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"months\":[0,6]},\"id\":\"1289\",\"type\":\"MonthsTicker\"},{\"attributes\":{\"num_minor_ticks\":5,\"tickers\":[{\"id\":\"1279\",\"type\":\"AdaptiveTicker\"},{\"id\":\"1280\",\"type\":\"AdaptiveTicker\"},{\"id\":\"1281\",\"type\":\"AdaptiveTicker\"},{\"id\":\"1282\",\"type\":\"DaysTicker\"},{\"id\":\"1283\",\"type\":\"DaysTicker\"},{\"id\":\"1284\",\"type\":\"DaysTicker\"},{\"id\":\"1285\",\"type\":\"DaysTicker\"},{\"id\":\"1286\",\"type\":\"MonthsTicker\"},{\"id\":\"1287\",\"type\":\"MonthsTicker\"},{\"id\":\"1288\",\"type\":\"MonthsTicker\"},{\"id\":\"1289\",\"type\":\"MonthsTicker\"},{\"id\":\"1290\",\"type\":\"YearsTicker\"}]},\"id\":\"1216\",\"type\":\"DatetimeTicker\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1242\",\"type\":\"Line\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"line_alpha\":{\"value\":0.1},\"size\":{\"units\":\"screen\",\"value\":2},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1246\",\"type\":\"Circle\"},{\"attributes\":{\"data_source\":{\"id\":\"1240\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1241\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1242\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"1244\",\"type\":\"CDSView\"}},\"id\":\"1243\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"axis_label\":\"Date\",\"formatter\":{\"id\":\"1276\",\"type\":\"DatetimeTickFormatter\"},\"ticker\":{\"id\":\"1216\",\"type\":\"DatetimeTicker\"}},\"id\":\"1215\",\"type\":\"DatetimeAxis\"},{\"attributes\":{},\"id\":\"1290\",\"type\":\"YearsTicker\"},{\"attributes\":{},\"id\":\"1291\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1292\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1293\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1294\",\"type\":\"Selection\"}],\"root_ids\":[\"1204\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"4c858d26-abcd-4f41-b728-5d5df9068418\",\"roots\":{\"1204\":\"e9626bdd-7362-4755-a07c-f125ff10e492\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1204"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make plot\n",
    "\n",
    "p = figure(x_axis_type='datetime', title='Monthly Average Revenue of Ocean Two',\n",
    "           plot_width=550, plot_height=350)\n",
    "p.yaxis.axis_label = 'Revenue'\n",
    "p.xaxis.axis_label = 'Date'\n",
    "# Predict 2019-01-01 onwards\n",
    "predict_region = BoxAnnotation(left=pd.to_datetime(\"2019-01-01\"),\n",
    "                               fill_alpha=0.1, fill_color=\"firebrick\")\n",
    "p.add_layout(predict_region)\n",
    "ppm400 = Span(location=400,\n",
    "              dimension='width', line_color='red',\n",
    "              line_dash='dashed', line_width=2)\n",
    "p.add_layout(ppm400)\n",
    "\n",
    "p.line(monthly_mean.index, monthly_mean['REVENUE'],\n",
    "       line_width=2, line_color=\"black\", alpha=0.5)\n",
    "p.circle(monthly_mean.index, monthly_mean['REVENUE'],\n",
    "         line_color=\"black\", alpha=0.1, size=2)\n",
    "\n",
    "train_label = Label(x=100, y=30, x_units='screen', y_units='screen',\n",
    "                    text='Training Set', render_mode='css', border_line_alpha=0.0,\n",
    "                    background_fill_alpha=0.0)\n",
    "test_label  = Label(x=510, y=80, x_units='screen', y_units='screen',\n",
    "                    text='Test Set', render_mode='css', border_line_alpha=0.0,\n",
    "                    background_fill_alpha=0.0)\n",
    "\n",
    "p.add_layout(train_label)\n",
    "p.add_layout(test_label)\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Gaussian Process (GP) model in PyMC3\n",
    "\n",
    "Below is the actual model. Each of the three component GPs is constructed separately. Since we are doing maximum a-posteriori  (MAP), we use Marginal GPs and lastly call the .marginal_likelihood method to specify the marginal posterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/pymc3/tuning/starting.py:61: UserWarning: find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.\n",
      "  warnings.warn('find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.')\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "  0%|          | 0/5000 [00:00<?, ?it/s]/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "logp = -27.723, ||grad|| = 0.017829: 100%|██████████| 300/300 [00:00<00:00, 444.67it/s] \n"
     ]
    }
   ],
   "source": [
    "# pull out normalized data\n",
    "t = data_early[\"t\"].values[:,None]\n",
    "y = data_early[\"y_n\"].values\n",
    "\n",
    "with pm.Model() as model:\n",
    "    # yearly periodic component x long term trend\n",
    "    η_per = pm.HalfCauchy(\"η_per\", beta=2, testval=1.0)\n",
    "    ℓ_pdecay = pm.Gamma(\"ℓ_pdecay\", alpha=10, beta=0.075)\n",
    "    period  = pm.Normal(\"period\", mu=1, sigma=0.05)\n",
    "    ℓ_psmooth = pm.Gamma(\"ℓ_psmooth \", alpha=4, beta=3)\n",
    "    cov_seasonal = η_per**2 * pm.gp.cov.Periodic(1, period, ℓ_psmooth) \\\n",
    "                            * pm.gp.cov.Matern52(1, ℓ_pdecay)\n",
    "    gp_seasonal = pm.gp.Marginal(cov_func=cov_seasonal)\n",
    "\n",
    "    # small/medium term irregularities\n",
    "    η_med = pm.HalfCauchy(\"η_med\", beta=0.5, testval=0.1)\n",
    "    ℓ_med = pm.Gamma(\"ℓ_med\", alpha=2, beta=0.75)\n",
    "    α = pm.Gamma(\"α\", alpha=5, beta=2)\n",
    "    cov_medium = η_med**2 * pm.gp.cov.RatQuad(1, ℓ_med, α)\n",
    "    gp_medium = pm.gp.Marginal(cov_func=cov_medium)\n",
    "\n",
    "    # long term trend\n",
    "    η_trend = pm.HalfCauchy(\"η_trend\", beta=2, testval=2.0)\n",
    "    ℓ_trend = pm.Gamma(\"ℓ_trend\", alpha=4, beta=0.1)\n",
    "    cov_trend = η_trend**2 * pm.gp.cov.ExpQuad(1, ℓ_trend)\n",
    "    gp_trend = pm.gp.Marginal(cov_func=cov_trend)\n",
    "\n",
    "    # noise model\n",
    "    η_noise = pm.HalfNormal(\"η_noise\", sigma=0.5, testval=0.05)\n",
    "    ℓ_noise = pm.Gamma(\"ℓ_noise\", alpha=2, beta=4)\n",
    "    σ  = pm.HalfNormal(\"σ\",  sigma=0.25, testval=0.05)\n",
    "    cov_noise = η_noise**2 * pm.gp.cov.Matern32(1, ℓ_noise) +\\\n",
    "                pm.gp.cov.WhiteNoise(σ)\n",
    "\n",
    "    # The Gaussian process is a sum of these three components\n",
    "    gp = gp_seasonal + gp_medium + gp_trend\n",
    "\n",
    "    # Since the normal noise model and the GP are conjugates, we use `Marginal` with the `.marginal_likelihood` method\n",
    "    y_ = gp.marginal_likelihood(\"y\", X=t, y=y, noise=cov_noise)\n",
    "\n",
    "    # this line calls an optimizer to find the MAP\n",
    "    mp = pm.find_MAP(include_transformed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['period:1.0085245409766752',\n",
       " 'α:1.988373307058695',\n",
       " 'η_med:0.1636945535018351',\n",
       " 'η_noise:0.00016401151534963817',\n",
       " 'η_per:1.7700970160225573',\n",
       " 'η_trend:0.002701133481886187',\n",
       " 'σ:0.2598854046366373',\n",
       " 'ℓ_med:1.3671454433337313',\n",
       " 'ℓ_noise:0.25012334444737233',\n",
       " 'ℓ_pdecay:120.15043410643221',\n",
       " 'ℓ_psmooth :0.808197481374807',\n",
       " 'ℓ_trend:30.004234056607558']"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display the results, dont show transformed parameter values\n",
    "sorted([name+\":\"+str(mp[name]) for name in mp.keys() if not name.endswith(\"_\")])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicting with gp ...\n",
      "Predicting with gp_trend ...\n",
      "Predicting with gp_medium ...\n",
      "Predicting with gp_seasonal ...\n",
      "Done\n"
     ]
    }
   ],
   "source": [
    "# predict at a 10 day granularity\n",
    "dates = pd.date_range(start='01/01/2016', end=\"01/01/2019\", freq=\"10D\")\n",
    "tnew = dates_to_idx(dates)[:,None]\n",
    "\n",
    "print(\"Predicting with gp ...\")\n",
    "mu, var = gp.predict(tnew, point=mp, diag=True)\n",
    "mean_pred = mu*std_rev + first_rev\n",
    "var_pred  = var*std_rev**2\n",
    "\n",
    "# make dataframe to store fit results\n",
    "fit = pd.DataFrame({\"t\": tnew.flatten(),\n",
    "                    \"mu_total\": mean_pred,\n",
    "                    \"sd_total\": np.sqrt(var_pred)},\n",
    "                   index=dates)\n",
    "\n",
    "print(\"Predicting with gp_trend ...\")\n",
    "mu, var = gp_trend.predict(tnew, point=mp,\n",
    "                           given={\"gp\": gp, \"X\": t, \"y\": y, \"noise\": cov_noise},\n",
    "                           diag=True)\n",
    "fit = fit.assign(mu_trend = mu*std_rev + first_rev,\n",
    "                 sd_trend = np.sqrt(var*std_rev**2))\n",
    "\n",
    "print(\"Predicting with gp_medium ...\")\n",
    "mu, var = gp_medium.predict(tnew, point=mp,\n",
    "                            given={\"gp\": gp, \"X\": t, \"y\": y, \"noise\": cov_noise},\n",
    "                            diag=True)\n",
    "fit = fit.assign(mu_medium = mu*std_rev + first_rev,\n",
    "                 sd_medium = np.sqrt(var*std_rev**2))\n",
    "\n",
    "print(\"Predicting with gp_seasonal ...\")\n",
    "mu, var = gp_seasonal.predict(tnew, point=mp,\n",
    "                              given={\"gp\": gp, \"X\": t, \"y\": y, \"noise\": cov_noise},\n",
    "                              diag=True)\n",
    "fit = fit.assign(mu_seasonal = mu*std_rev + first_rev,\n",
    "                 sd_seasonal = np.sqrt(var*std_rev**2))\n",
    "print(\"Done\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
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LlYORAnjqdXEI740A=\",\"dtype\":\"float64\",\"shape\":[220]}},\"selected\":{\"id\":\"3045\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3044\",\"type\":\"UnionRenderers\"}},\"id\":\"3015\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"2977\",\"type\":\"PanTool\"},{\"id\":\"2978\",\"type\":\"WheelZoomTool\"},{\"id\":\"2979\",\"type\":\"BoxZoomTool\"},{\"id\":\"2980\",\"type\":\"SaveTool\"},{\"id\":\"2981\",\"type\":\"ResetTool\"},{\"id\":\"2982\",\"type\":\"HelpTool\"}]},\"id\":\"2983\",\"type\":\"Toolbar\"}],\"root_ids\":[\"2956\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"97371637-55ba-4f86-9185-70366bfaa1e9\",\"roots\":{\"2956\":\"b9ac3d83-189b-4fa1-bcd2-afb31b35965e\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "2956"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## plot the components\n",
    "p = figure(title=\"Decomposition of the Revenue\",\n",
    "           x_axis_type='datetime', plot_width=750, plot_height=550)\n",
    "p.yaxis.axis_label = 'Revenue'\n",
    "p.xaxis.axis_label = 'Date'\n",
    "\n",
    "# plot mean and 2σ region of total prediction\n",
    "upper = fit.mu_total + 2*fit.sd_total\n",
    "lower = fit.mu_total - 2*fit.sd_total\n",
    "band_x = np.append(fit.index.values, fit.index.values[::-1])\n",
    "band_y = np.append(lower, upper[::-1])\n",
    "\n",
    "# total fit\n",
    "p.line(fit.index, fit.mu_total,\n",
    "       line_width=1, line_color=\"firebrick\", legend=\"Total fit\")\n",
    "p.patch(band_x, band_y,\n",
    "        color=\"firebrick\", alpha=0.6, line_color=\"white\")\n",
    "\n",
    "# trend\n",
    "p.line(fit.index, fit.mu_trend,\n",
    "       line_width=1, line_color=\"blue\", legend=\"Long term trend\")\n",
    "\n",
    "# medium\n",
    "p.line(fit.index, fit.mu_medium,\n",
    "       line_width=1, line_color=\"green\", legend=\"Medium range variation\")\n",
    "\n",
    "# seasonal\n",
    "p.line(fit.index, fit.mu_seasonal,\n",
    "       line_width=1, line_color=\"orange\", legend=\"Seasonal process\")\n",
    "\n",
    "# true value\n",
    "p.circle(data_early.index, data_early['REVENUE'],\n",
    "         color=\"black\", legend=\"Observed data\")\n",
    "p.legend.location = \"bottom_left\"\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicting year 2019\n",
      "Predicting year 2020\n",
      "Predicting year 2021\n",
      "Predicting year 2023\n",
      "Predicting year 2025\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"6abe4e2f-7d74-496c-8045-f41597152f23\" data-root-id=\"4378\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"ecad61b0-e4d8-450d-8eaa-1a75620eaf12\",\"roots\":{\"4378\":\"6abe4e2f-7d74-496c-8045-f41597152f23\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "4378"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot several years \n",
    "\n",
    "p = figure(title=\"Several years of the seasonal component\",\n",
    "           plot_width=550, plot_height=350)\n",
    "p.yaxis.axis_label = 'Δ Revenue'\n",
    "p.xaxis.axis_label = 'Month'\n",
    "\n",
    "colors = brewer['Paired'][5]\n",
    "years = [\"2019\", \"2020\", \"2021\", \"2023\", \"2025\"]\n",
    "\n",
    "for i, year in enumerate(years):\n",
    "    dates = pd.date_range(start=\"1/1/\"+year, end=\"12/31/\"+year, freq=\"10D\")\n",
    "    tnew = dates_to_idx(dates)[:,None]\n",
    "\n",
    "    print(\"Predicting year\", year)\n",
    "    mu, var = gp_seasonal.predict(tnew, point=mp, diag=True,\n",
    "                                  given={\"gp\": gp, \"X\": t, \"y\": y, \"noise\": cov_noise})\n",
    "    mu_pred = mu*std_rev\n",
    "\n",
    "    # plot mean\n",
    "    x = np.asarray((dates - dates[0])/pd.Timedelta(1, \"M\")) + 1\n",
    "    p.line(x, mu_pred,\n",
    "           line_width=1, line_color=colors[i], legend=year)\n",
    "\n",
    "p.legend.location = \"bottom_left\"\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forecast into future years"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sampling gp predictions ...\n"
     ]
    }
   ],
   "source": [
    "dates = pd.date_range(start=\"01/01/2016\", end=\"12/31/2021\", freq=\"10D\")\n",
    "tnew = dates_to_idx(dates)[:,None]\n",
    "\n",
    "print(\"Sampling gp predictions ...\")\n",
    "mu_pred, cov_pred = gp.predict(tnew, point=mp)\n",
    "\n",
    "# draw samples, and rescale\n",
    "n_samples = 2000\n",
    "samples = pm.MvNormal.dist(mu=mu_pred, cov=cov_pred).random(size=n_samples)\n",
    "samples = samples * std_rev + first_rev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_total = pd.concat([data_early, data_later], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"ccedd4d4-1f8e-411a-83f7-7e22c75c8f08\" data-root-id=\"3899\"></div>\n"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
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fit\"},\"renderers\":[{\"id\":\"3934\",\"type\":\"GlyphRenderer\"}]},\"id\":\"3956\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"3994\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"days\":[1,4,7,10,13,16,19,22,25,28]},\"id\":\"3946\",\"type\":\"DaysTicker\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"3914\",\"type\":\"BasicTicker\"}},\"id\":\"3917\",\"type\":\"Grid\"},{\"attributes\":{\"source\":{\"id\":\"3967\",\"type\":\"ColumnDataSource\"}},\"id\":\"3971\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"3941\",\"type\":\"BasicTickFormatter\"}],\"root_ids\":[\"3899\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"1219d239-026d-42b4-bf76-854f0536e960\",\"roots\":{\"3899\":\"ccedd4d4-1f8e-411a-83f7-7e22c75c8f08\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "3899"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### make plot\n",
    "p = figure(x_axis_type='datetime', plot_width=700, plot_height=400)\n",
    "p.yaxis.axis_label = 'Revenue'\n",
    "p.xaxis.axis_label = 'Date'\n",
    "\n",
    "### plot mean and 2σ region of total prediction\n",
    "# scale mean and var\n",
    "mu_pred_sc = mu_pred * std_rev + first_rev\n",
    "sd_pred_sc = np.sqrt(np.diag(cov_pred) * std_rev**2 )\n",
    "\n",
    "upper = mu_pred_sc + 2*sd_pred_sc\n",
    "lower = mu_pred_sc - 2*sd_pred_sc\n",
    "band_x = np.append(dates, dates[::-1])\n",
    "band_y = np.append(lower, upper[::-1])\n",
    "\n",
    "p.line(dates, mu_pred_sc,\n",
    "       line_width=2, line_color=\"firebrick\", legend=\"Total fit\")\n",
    "p.patch(band_x, band_y,\n",
    "        color=\"firebrick\", alpha=0.6, line_color=\"white\")\n",
    "\n",
    "# some predictions\n",
    "idx = np.random.randint(0, samples.shape[0], 10)\n",
    "p.multi_line([dates]*len(idx), [samples[i,:] for i in idx],\n",
    "             color=\"firebrick\", alpha=0.5, line_width=0.5)\n",
    "# true value\n",
    "#p.line(data_later.index, data_later['CO2'],\n",
    "#       line_width=2, line_color=\"black\", legend=\"Observed data\")\n",
    "p.circle(data_total.index, data_total['REVENUE'],\n",
    "         color=\"black\", legend=\"Observed data\")\n",
    "\n",
    "ppm400 = Span(location=400,\n",
    "              dimension='width', line_color='black',\n",
    "              line_dash='dashed', line_width=1)\n",
    "p.add_layout(ppm400)\n",
    "p.legend.location = \"bottom_right\"\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.7"
  }
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