Ch09a_MonteCarlo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Monte Carlo Simulations\n",
    "\n",
    "This notebook shows examples of Monte Carlo simulations for: *(a)* the distribution from a GARCH process; *(b)* the effect of heteroskedasticity on OLS standard errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions\n",
    "\n",
    "The key functions for simulations are coded in this notebook. However, the function for OLS is from the (local) `FinEcmt_OLS` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "MyModulePath = joinpath(pwd(),\"jlFiles\")\n",
    "!in(MyModulePath,LOAD_PATH) && push!(LOAD_PATH,MyModulePath);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using FinEcmt_OLS, Random, Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots, LaTeXStrings\n",
    "\n",
    "gr(size=(480,320))\n",
    "default(fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulating the Distribution of a GARCH(1,1) Variable\n",
    "\n",
    "The `GarchSim(T,ω,α,β)` function (see below) generates $T$ observations of a variable $u_t$ whose conditional distribution (based on information in $t-1$) is $N(0,\\sigma_t^2)$, where $\\sigma_t^2$ follows a GARCH(1,1) process:\n",
    "\n",
    "$\n",
    "\\sigma_{t}^{2}    =\\omega+\\alpha u_{t-1}^{2}+\\beta\\sigma_{t-1}^{2}.\n",
    "$\n",
    "\n",
    "The subsequent cells call on the `GarchSim()` function and plots a histogram of the simulated values. This is repeated for two different values of $\\alpha$: a high value and a low value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GarchSim"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "    GarchSim(T,ω,α,β)\n",
    "\n",
    "Simulate a time series of T residuals from a GARCH(1,1) process.\n",
    "\n",
    "### Remark\n",
    "- The vector of σ² values is not exported from the function. If needed, this could easily be changed.\n",
    "\n",
    "\"\"\"\n",
    "function GarchSim(T,ω,α,β)\n",
    "\n",
    "    (σ²,u) = [zeros(T) for i=1:2]\n",
    "    σ²[1]  = ω/(1-α-β)                              #average σ² as starting value\n",
    "    for t = 2:T\n",
    "        σ²[t] = ω + α*u[t-1]^2 + β*σ²[t-1]\n",
    "        u[t]  = sqrt(σ²[t])*randn()\n",
    "    end\n",
    "\n",
    "    return u\n",
    "\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[31m\u001b[1mthe histogram is clearly non-N()\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "(T,ω,α,β) = (200_000,1,0.19,0.8)                #fairly high α value\n",
    "\n",
    "Random.seed!(123456)                            #to replicate the same random numbers\n",
    "u = GarchSim(T,ω,α,β)\n",
    "\n",
    "(qL,qH) = quantile(u,[0.001,0.999])             #quantiles 0.001 and 0.999\n",
    "\n",
    "uGrid = range(qL,qH,length=101)                 #a grid of values between the quantiles\n",
    "pdfNu = pdf.(Normal(mean(u),std(u)),uGrid)      #best fitting N() as a comparison\n",
    "\n",
    "p1 = histogram( u,\n",
    "                bins = uGrid,\n",
    "                fillcolor = :pink,\n",
    "                normalized = true,\n",
    "                label = \"histogram\",\n",
    "                title = L\"\\mathrm{Distribution \\ of \\ GARCH(1,1), \\ } \\alpha =0.19\" )\n",
    "plot!(uGrid,pdfNu,color=:blue,label=\"best N()\")\n",
    "display(p1)\n",
    "\n",
    "printred(\"the histogram is clearly non-N()\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[31m\u001b[1mthe histogram looks almost N()\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "α = 0.09                                            #lower α\n",
    "\n",
    "Random.seed!(123456)\n",
    "u = GarchSim(T,ω,α,β)\n",
    "\n",
    "(qL,qH) = quantile(u,[0.001,0.999])\n",
    "\n",
    "uGrid = range(qL,qH,length=101)\n",
    "pdfNu = pdf.(Normal(mean(u),std(u)),uGrid)\n",
    "\n",
    "p1 = histogram( u,\n",
    "                bins = uGrid,\n",
    "                fillcolor = :lightblue,\n",
    "                normalized = true,\n",
    "                label = \"histogram\",\n",
    "                title = L\"\\mathrm{Distribution \\ of \\ GARCH(1,1), \\ } \\alpha =0.09\" )\n",
    "plot!(uGrid,pdfNu,color=:blue,label=\"best N()\")\n",
    "display(p1)\n",
    "\n",
    "printred(\"the histogram looks almost N()\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulating (White's) Heteroskedasticity in OLS\n",
    "\n",
    "The `SimOL(NSim,T,α)` function (see below) first simulates `T` observations where the residuals in an OLS regression are heteroskedastic, since they are generated as \n",
    "\n",
    "$\n",
    "\\epsilon_t = u_t (1+\\alpha |f_t|),\n",
    "$\n",
    "\n",
    "where $u_t$ is $N(0,1)$ and $f_t$ is a regressor.\n",
    "\n",
    "The function then estimates the traditional OLS standard errors and also White's standard errors.\n",
    "\n",
    "The subsequent cell compares the different standard errors in two cases: $\\alpha=0$ and $\\alpha=1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SimOLS"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "    SimOLS(NSim,T,α)\n",
    "\n",
    "Simulate data for a regression model with heteroskedastic errors and then estimate both point estimates\n",
    "and standard errors according to traditional OLS (Gauss-Markov) and White.\n",
    "\n",
    "### Input\n",
    "- `NSim::Int`:    number of simulations (eg. 3000)\n",
    "- `T::Int`:       sample length (eg. 200)\n",
    "- `α::Number`:    degree of heteroskedasticity\n",
    "\n",
    "\"\"\"\n",
    "function SimOLS(NSim,T,α)\n",
    "\n",
    "    (bLS,StdLS,StdWhite) = [fill(NaN,NSim) for i = 1:3]\n",
    "    for i = 1:NSim\n",
    "        f = randn(T)                           #some random regressors\n",
    "        ϵ = randn(T) .* (1 .+ α*abs.(f))       #heteroskedastic residuals\n",
    "        y = 1 .+ 0.9*f + ϵ\n",
    "        x = [f ones(T)]\n",
    "        (b,u,) = OlsGM(y,x)                 #OLS, point estimates\n",
    "        bLS[i] = b[1]\n",
    "        Sxx         = x'x\n",
    "        S           = (x.*u)'*(x.*u)\n",
    "        V_W         = inv(Sxx)'S*inv(Sxx)      #Cov(b), White\n",
    "        StdWhite[i] = sqrt(V_W[1,1])\n",
    "        V_iid       = inv(Sxx)*var(u)          #OLS, traditional\n",
    "        StdLS[i]    = sqrt(V_iid[1,1])\n",
    "    end\n",
    "\n",
    "    return bLS, StdLS, StdWhite\n",
    "\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mStd of slope when α=0:\u001b[22m\u001b[39m\n",
      "\n",
      " Simulated       OLS     White\n",
      "     0.071     0.071     0.070\n",
      "\n",
      "\u001b[31m\u001b[1mthe standard errors are similar\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "NSim = 25000           #number of simulated samples\n",
    "T    = 200             #sample size\n",
    "\n",
    "α = 0                  #no heteroskedasticity\n",
    "Random.seed!(123456)\n",
    "(bLS,StdLS,StdWhite) = SimOLS(NSim,T,α)\n",
    "\n",
    "printblue(\"Std of slope when α=$(α):\\n\")\n",
    "printmat(std(bLS),mean(StdLS),mean(StdWhite);colNames=[\"Simulated\",\"OLS\",\"White\"])\n",
    "\n",
    "printred(\"the standard errors are similar\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mStd of slope when α=1:\u001b[22m\u001b[39m\n",
      "\n",
      " Simulated       OLS     White\n",
      "     0.188     0.134     0.185\n",
      "\n",
      "\u001b[31m\u001b[1mthe standard errors are clearly different\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "α = 1                  #lots of heteroskedasticity\n",
    "Random.seed!(123456)\n",
    "(bLS,StdLS,StdWhite) = SimOLS(NSim,T,α)\n",
    "\n",
    "printblue(\"Std of slope when α=$(α):\\n\")\n",
    "printmat(std(bLS),mean(StdLS),mean(StdWhite);colNames=[\"Simulated\",\"OLS\",\"White\"])\n",
    "\n",
    "printred(\"the standard errors are clearly different\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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