Ch13_TimeSeries.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time Series Analysis\n",
    "\n",
    "This notebook estimates autocorrelations and different time series models (AR, MA and VAR)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Load Packages and Extra Functions\n",
    "\n",
    "The key functions in this notebook are from the (local) `FinEcmt_TimeSeries` module, but we also use [StatsBase.jl](https://github.com/JuliaStats/StatsBase.jl) package for estimating autocorrelations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "MyModulePath = joinpath(pwd(),\"src\")\n",
    "!in(MyModulePath,LOAD_PATH) && push!(LOAD_PATH,MyModulePath);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "using DelimitedFiles, LinearAlgebra, Distributions, StatsBase\n",
    "using FinEcmt_OLS\n",
    "using FinEcmt_TimeSeries: ARMAFilter, ARpEst, MAqLL, VARFilter, CompanionFormAR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "using Plots\n",
    "default(size = (480,320),fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size: 574\n"
     ]
    }
   ],
   "source": [
    "xx  = readdlm(\"Data/RvSP500.csv\",',',skipstart=1)\n",
    "y   = xx[:,3]            #SP500 log realized monthly volatility\n",
    "xx  = nothing\n",
    "\n",
    "T   = size(y,1)\n",
    "println(\"Sample size: $T\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Descriptive Statistics\n",
    "\n",
    "## Autocorrelations\n",
    "\n",
    "The $s\\text{th}$ autocorrelation $\\rho_s$ is the correlation of $y_{t}$ and $y_{t-s}$. It is a useful tool for describing the properties of data.\n",
    "\n",
    "It can be shown that the t-stat of an autocorrelation is $\\sqrt{T} \\rho_s$.\n",
    "\n",
    "We can (jointly) test the first $L$ autocorrelations by the Box-Pierce test, which (under the null hypothesis of no autocorrelation) has a $\\chi^2_L$ distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mAutocorrelations:\u001b[22m\u001b[39m\n",
      "\n",
      "lag autocorrr    t-stat\n",
      "1       0.709    16.982\n",
      "2       0.602    14.419\n",
      "3       0.529    12.684\n",
      "4       0.459    11.000\n",
      "5       0.455    10.903\n",
      "\n",
      "\u001b[34m\u001b[1mBox-Pierce test:\u001b[22m\u001b[39m\n",
      "\n",
      "test statistic       897.040     9.236\n",
      "\n"
     ]
    }
   ],
   "source": [
    "L = 5\n",
    "lags = 1:L\n",
    "ρ = autocor(y,lags)         #using the StatsBase package\n",
    "\n",
    "printblue(\"Autocorrelations:\\n\")\n",
    "printmat(ρ,sqrt(T)*ρ;colNames=[\"autocorrr\",\"t-stat\"],rowNames=lags,cell00=\"lag\")\n",
    "\n",
    "BP = T*sum(ρ.^2)            #the Box-Pierce test statistic\n",
    "\n",
    "printblue(\"Box-Pierce test:\\n\")\n",
    "printmat(BP,quantile(Chisq(L),0.9);rowNames=[\"test statistic\",\"10% critical value\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# White Noise\n",
    "\n",
    "A white noise process is supposed to have no autocorrelation and have fixed means and volatilities, so the only parameters are the mean and the standard deviation (or variance).\n",
    "\n",
    "Estimation: traditional sample mean and standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean and std:     2.567     0.437\n"
     ]
    }
   ],
   "source": [
    "μ = mean(y)\n",
    "σ = std(y)\n",
    "\n",
    "printlnPs(\"Mean and std:\",μ,σ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# AR(p)\n",
    "\n",
    "This section discusses the properties and estimation of autoregressive (AR) processes.\n",
    "\n",
    "## Impulse Response Function of AR Processes\n",
    "\n",
    "The next cell shows how a shock to an AR process propagates over time, the *impulse response function*. This is a useful tool for understanding the properties of the model.\n",
    "\n",
    "The two models used here are an AR(1)\n",
    "\n",
    "$\n",
    "y_t = a y_{t-1} + \\epsilon_t\n",
    "$\n",
    "\n",
    "and an AR(2)\n",
    "\n",
    "$\n",
    "y_t = a_1 y_{t-1} + a_2 y_{t-2} + \\epsilon_t.\n",
    "$\n",
    "\n",
    "The impulse response function is calculated by setting $\\epsilon_0=1$ but all other $\\epsilon_t=0$ and then looping over time. For *stationary models*, the impulse response function eventually converges to zero. That is, the effect of a shock eventually disappears.\n",
    "\n",
    "\n",
    "### A Remark on the Code\n",
    "\n",
    "- To be consistent with the lecture notes, the shock will happen in period 0, which will correspond to `ϵ[3]` below. Notice that typical Julia vectors starts at index 1. (The [OffsetArrays.jl](https://github.com/JuliaArrays/OffsetArrays.jl) package allows more flexible indexing, but it's not used here.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mThe impulse responses:\u001b[22m\u001b[39m\n",
      "\n",
      "period     AR(1)     AR(2)\n",
      "-2         0.000     0.000\n",
      "-1         0.000     0.000\n",
      "0          1.000     1.000\n",
      "1          0.850     0.850\n",
      "2          0.722     0.222\n",
      "3          0.614    -0.236\n",
      "4          0.522    -0.312\n",
      "5          0.444    -0.147\n",
      "6          0.377     0.031\n",
      "7          0.321     0.100\n",
      "8          0.272     0.069\n",
      "\n",
      "\u001b[31m\u001b[1mHowever, we only plot period 0 and onwards\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "a = 0.85               #AR(1)\n",
    "(a₁,a₂) = (0.85,-0.5)  #AR(2)\n",
    "\n",
    "τ_max  = 11\n",
    "period = -2:(τ_max-3)       #-2,-1,0,1,...\n",
    "\n",
    "ϵ    = zeros(τ_max)\n",
    "ϵ[3] = 1                     #a single shock at period=0, which is at index τ=3, otherwise zeros\n",
    "\n",
    "(y1,y2) = (copy(ϵ),copy(ϵ))\n",
    "for τ = 3:τ_max                 #loop starts at τ=3 (period=0)\n",
    "    y1[τ] = a*y1[τ-1] + ϵ[τ]\n",
    "    y2[τ] = a₁*y2[τ-1] + a₂*y2[τ-2] + ϵ[τ]\n",
    "end\n",
    "\n",
    "printblue(\"The impulse responses:\\n\")\n",
    "printmat([y1 y2];colNames=[\"AR(1)\",\"AR(2)\"],rowNames=period,cell00=\"period\")\n",
    "\n",
    "printred(\"However, we only plot period 0 and onwards\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( period,[y1 y2],\n",
    "           label = [\"AR(1)\" \"AR(2)\"],\n",
    "           linecolor = [:red :blue],\n",
    "           linestyle = [:solid :dash],\n",
    "           xticks = period,\n",
    "           xlims = (0,8),                  #plot only period 0-\n",
    "           xlabel = \"period\",\n",
    "           title = \"Impuse response function (IRF)\",\n",
    "           annotation = (1.3,-0.2,text(\"shock in period 0\",8)) )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Roots of an AR Model (extra)\n",
    "\n",
    "The *roots* of an AR(p) is a formal way of determining whether it is stationary. (A informal way is to check whether the impulse response function goes to zero as the horizon is extended.)\n",
    "\n",
    "An easy way to calculate the roots is to first transform the AR(p) to a V(ector)AR(1) (also called companion form) and then calculate the eigenvalues. If their absolute values are lower than one, then the model is stationary.\n",
    "\n",
    "For instance, an AR(2)\n",
    "\n",
    "$\n",
    "y_t = a_1 y_{t-1} + a_2 y_{t-2} + \\epsilon_t.\n",
    "$\n",
    "\n",
    "can be written as a 2-variable VAR(1) \n",
    "\n",
    "$\n",
    "z_t = A_1 z_{t-1} + u_t,\n",
    "$\n",
    "\n",
    "where \n",
    "\n",
    "$\n",
    "z_t = \n",
    "\\begin{bmatrix} \n",
    "y_t \\\\ \n",
    "y_{t-1}  \n",
    "\\end{bmatrix} \n",
    "\\text{ and }\n",
    "A_1 = \n",
    "\\begin{bmatrix} \n",
    "a_1 & a_2\\\\ \n",
    "1 & 0 \n",
    "\\end{bmatrix}.\n",
    "$\n",
    "\n",
    "This is done in the `CompanionFormAR(a)` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "absolute values of the eigenvalues: should be < 1 for stationarity\n",
      "     0.707\n",
      "     0.707\n",
      "\n"
     ]
    }
   ],
   "source": [
    "λ = eigen(CompanionFormAR([a₁,a₂])).values    #eigenvalues of the companion form\n",
    "\n",
    "println(\"absolute values of the eigenvalues: should be < 1 for stationarity\")\n",
    "printmat(abs.(λ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimation of an AR Process\n",
    "\n",
    "AR models can be estimated by OLS. \n",
    "\n",
    "The `ARpEst(y,p)` function (included above) provides a simple way of doing this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "```\n",
       "ARpEst(y,p)\n",
       "```\n",
       "\n",
       "Estimate an AR(p) model (with an intercept) on the data in a vector `y`.\n",
       "\n",
       "Output: the slope coefficients (not the intercept).\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@doc2 ARpEst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#using CodeTracking\n",
    "#println(@code_string ARpEst([1],2))    #print the source code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated AR(1) coef:      0.713\n",
      "Estimated AR(2) coefs:      0.569     0.204\n"
     ]
    }
   ],
   "source": [
    "aAR1 = ARpEst(y,1)\n",
    "aAR2 = ARpEst(y,2)\n",
    "\n",
    "printlnPs(\"Estimated AR(1) coef: \",aAR1)\n",
    "printlnPs(\"Estimated AR(2) coefs: \",aAR2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forecasting with an AR Process\n",
    "\n",
    "Forecasts can be calculated recursively. For instance, for an AR(2) and data on $(y_{-1},y_0$), we can calculate the forecast for $t=1$ as \n",
    "\n",
    "$\n",
    "\\textrm{E}_0 y_1 = a_1 y_0 + a_2 y_{-1}.\n",
    "$\n",
    "\n",
    "Then, the forecast for $t=2$ (still based on the information in $t=0$) is \n",
    "\n",
    "$\n",
    "\\textrm{E}_0 y_2 = a_1 \\textrm{E}_0 y_1 + a_2 y_0,\n",
    "$\n",
    "\n",
    "where $\\textrm{E}_0 y_1$ is from the first forecast.\n",
    "\n",
    "Since $\\textrm{E}_0 y_0 = y_0$, this can be written on a recursive form as \n",
    "\n",
    "$\n",
    "\\textrm{E}_0 y_\\tau = a_1 \\textrm{E}_0 y_{\\tau-1} + a_2 \\textrm{E}_0 y_{\\tau-2}.\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.85               #AR(1)\n",
    "(a₁,a₂) = (0.85,-0.5)  #AR(2)\n",
    "\n",
    "τ_max  = 11\n",
    "period = -2:(τ_max-3)       #-2,-1,0,1,...\n",
    "\n",
    "y1    = zeros(τ_max)                  #forecasts from AR(1)\n",
    "y1[3] = 3\n",
    "for τ = 4:τ_max                       #loop starts at τ=4 (period=1)\n",
    "    y1[τ] = a*y1[τ-1]\n",
    "end\n",
    "\n",
    "y2      = zeros(τ_max)                #forecast from AR(2)\n",
    "y2[2:3] = [1,3]\n",
    "for τ = 4:τ_max                       #loop starts at τ=4 (period=1)\n",
    "    y2[τ] = a₁*y2[τ-1] + a₂*y2[τ-2]\n",
    "end\n",
    "\n",
    "p1 = plot( [period period],[y1 y2],\n",
    "           label = [\"AR(1), y₀(0) = 3\" \"AR(2), (y₋₁,y₀) = (1,3)\"],\n",
    "           linecolor = [:red :blue],\n",
    "           linestyle = [:solid :dash],\n",
    "           xticks = period,\n",
    "           xlims = (0,8),            #plotting period 0 and onwards\n",
    "           xlabel = \"period\",\n",
    "           title = \"Forecasts based on t=0 info\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Remark on the Code\n",
    "\n",
    "- As an alternative to the loop, the `ARMAFilter()` funtion can be used instead. Notice that this function cuts the initial values, so the results need to padded with those.\n",
    "\n",
    "The function simulates `ARMA(p,q)` models. For instance, an `ARMA(1,1)` is\n",
    "\n",
    "$ y_t = \\rho y_{t-1} + \\theta_0 \\epsilon_{t} + \\theta \\epsilon_{t-1}$,\n",
    "\n",
    "where $\\theta_0$ is the coefficient of the period-$t$ shock (often 1), while $\\rho$ and $\\theta$ (possibly vectors) are the coefficients for the AR and MA parts, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "```\n",
       "ARMAFilter(ϵ,rho=[],θ=[],θ₀=1.0,y₀=[])\n",
       "```\n",
       "\n",
       "Calculate ARMA(p,q) transformation of an input series ϵ. Uses explicit loop (instead of DSP.filt).\n",
       "\n",
       "### Input\n",
       "\n",
       "  * `ϵ::Vector`:      T-vector with an input series\n",
       "  * `rho::Vector`:    (optional) p-vector of autoregression coefficients, could be []\n",
       "  * `θ::Vector`:      (optional) q-vector of moving average coefficients (lag 1 to q), could be []\n",
       "  * `θ₀::Number`:     (optional) scalar, coefficient on ϵ[t] in MA part, [1]\n",
       "  * `y₀::Vector`:     (optional) p-vector, initial values of y, eg. [y(-1);y(0)], default: zeros(p)\n",
       "\n",
       "### Output\n",
       "\n",
       "  * `y::Vector`:      T-vector with output from the filter\n",
       "\n",
       "### Notice\n",
       "\n",
       "1. The process is `y[t] = rho[1]*y[t-1] + ... + rho[p]*y[t-p] + θ₀*ϵ[t]  +  θ[1]*ϵ[t-1] + ... + θ[q]*ϵ[t-q]`\n",
       "2. The initial values of `ϵ` are assumed to be zero\n",
       "3. To calculate impulse response functions, use `ϵ = [1;zeros(T-1,1)]`\n",
       "4. There are no initial values in a pure MA and the case of `q > p` is handled with padding with zeros (see the code below)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@doc2 ARMAFilter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#using CodeTracking\n",
    "#println(@code_string ARMAFilter([1],[1]))    #print the source code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mWe can also use the ARMAFilter() function to do the forecasts:\u001b[22m\u001b[39m\n",
      "\n",
      "period         loop ARMAFilter()\n",
      "-2            0.000        0.000\n",
      "-1            1.000        1.000\n",
      "0             3.000        3.000\n",
      "1             2.050        2.050\n",
      "2             0.242        0.242\n",
      "3            -0.819       -0.819\n",
      "4            -0.817       -0.817\n",
      "5            -0.285       -0.285\n",
      "6             0.166        0.166\n",
      "7             0.284        0.284\n",
      "8             0.158        0.158\n",
      "\n"
     ]
    }
   ],
   "source": [
    "y2b = ARMAFilter(zeros(τ_max-3),[a₁,a₂],[],1,[1,3])\n",
    "y2b = [0;1;3;y2b]             #pad with the initial values\n",
    "\n",
    "printblue(\"We can also use the ARMAFilter() function to do the forecasts:\\n\")\n",
    "printmat(y2,y2b;colNames=[\"loop\",\"ARMAFilter()\"],rowNames=-2:8,cell00=\"period\",width=13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More Descriptive Statistics: Partial Autocorrelations\n",
    "\n",
    "The partial autocorrelation coefficient is the regression coefficients on $x_{t-p}$ in an AR(p) regression, that is, on the last regressor. It is a useful tool for describing the properties of your data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mautocorrelations and  partial autocorrelations:\u001b[22m\u001b[39m\n",
      "\n",
      "lag  autocorr       pac\n",
      "1       0.709     0.713\n",
      "2       0.602     0.204\n",
      "3       0.529     0.103\n",
      "4       0.459     0.031\n",
      "5       0.455     0.130\n",
      "\n",
      "\u001b[31m\u001b[1mρ[1] and pac[1] are very similar: in a large sample they would be almost the same\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "pac = pacf(y,lags)        #from the StatsBase package\n",
    "\n",
    "printblue(\"autocorrelations and  partial autocorrelations:\\n\")\n",
    "printmat(ρ,pac;colNames=[\"autocorr\",\"pac\"],rowNames=lags,cell00=\"lag\")\n",
    "\n",
    "printred(\"ρ[1] and pac[1] are very similar: in a large sample they would be almost the same\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MA(q)\n",
    "\n",
    "This section discusses the properties and estimation of moving average (MA) processes.\n",
    "\n",
    "## The Impulse Response Function of an MA(q) Process\n",
    "\n",
    "goes to zero at lag $q+1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "θ = 0.5              #MA(1)\n",
    "(θ₁,θ₂) = (0.5,0.3)  #MA(2)\n",
    "\n",
    "τ_max  = 11\n",
    "period = -2:(τ_max-3)       #-2,-1,0,1,...\n",
    "\n",
    "ϵ    = zeros(τ_max)\n",
    "ϵ[3] = 1                     #a single shock, otherwise zeros\n",
    "\n",
    "(y1,y2) = (copy(ϵ),copy(ϵ))  #MA(1) and MA(2)\n",
    "for τ = 3:τ_max              #loop starts at τ=3 (period=0)\n",
    "    y1[τ] = ϵ[τ] + θ*ϵ[τ-1]\n",
    "    y2[τ] = ϵ[τ] + θ₁*ϵ[τ-1] + θ₂*ϵ[τ-2]   #or y2=ARMAFilter(ϵ,[],[θ₁,θ₂])\n",
    "end\n",
    "\n",
    "p1 = plot( period,[y1 y2],\n",
    "           label = [\"MA(1)\" \"MA(2)\"],\n",
    "           linecolor = [:red :blue],\n",
    "           linestyle = [:solid :dash],\n",
    "           xticks = period,\n",
    "           xlims = (0,8),        #period 0 and onwards\n",
    "           xlabel = \"period\",\n",
    "           title = \"IRF\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimation of an MA(q) (extra)\n",
    "\n",
    "To estimate an MA model, we can apply MLE. For the numerical optimization we use the [Optim.jl](https://github.com/JuliaNLSolvers/Optim.jl) package. \n",
    "\n",
    "The `MAqLL(par,y)` function (included above) calculates the likelihood function and returns it as its first output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mMLE of MA(4):\u001b[22m\u001b[39m\n",
      "\n",
      "       parameters\n",
      "θ₁          1.458\n",
      "θ₂          1.552\n",
      "θ₃          1.170\n",
      "θ₄          0.516\n",
      "σ           0.638\n",
      "\n"
     ]
    }
   ],
   "source": [
    "using Optim\n",
    "\n",
    "par0 = [0.5,0.3,0,0,1]   #θ₁,θ₂,θ₃,θ₄,σ         #estimate an MA(4)\n",
    "Sol  = optimize(par->-MAqLL(par,y)[1],par0)     #minimize -LL\n",
    "\n",
    "θ = Optim.minimizer(Sol)[1:end-1]\n",
    "σ = Optim.minimizer(Sol)[end]\n",
    "\n",
    "printblue(\"MLE of MA(4):\\n\")\n",
    "printmat([θ;σ];colNames=[\"parameters\"],rowNames=[\"θ₁\",\"θ₂\",\"θ₃\",\"θ₄\",\"σ\"],width=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "absolute values of the eigenvalues: should be < 1 for MLE to be valid\n",
      "     0.798\n",
      "     0.798\n",
      "     0.901\n",
      "     0.901\n",
      "\n"
     ]
    }
   ],
   "source": [
    "λ = eigen(CompanionFormAR(-θ)).values    #eigenvalues of the companion form\n",
    "\n",
    "println(\"absolute values of the eigenvalues: should be < 1 for MLE to be valid\")\n",
    "printmat(abs.(λ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# VAR(p)\n",
    "\n",
    "This section discusses the properties and estimation of vector autoregressive (VAR) processes.\n",
    "\n",
    "## Impulse Response Function of a VAR(1) Process\n",
    "\n",
    "The cells below shows the impulse response function for a 2-variable VAR(1)\n",
    "\n",
    "$\n",
    "y_t = A_1 y_{t-1} + \\epsilon_t,\n",
    "$\n",
    "\n",
    "where $y_t$ and $y_{t-1}$ are vectors with two elements and\n",
    "\n",
    "$\n",
    "A_1 = \n",
    "\\begin{bmatrix} \n",
    "0.5 & 0.2\\\\ \n",
    "0.1 & -0.3 \n",
    "\\end{bmatrix}.\n",
    "$\n",
    "\n",
    "The code calls on the function `VARFilter()`, which was included at the top of the notebook. It is similar to the `ARMAFilter()`, but it handles only VAR models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "```\n",
       "VARFilter(ϵ,A,y₀)\n",
       "```\n",
       "\n",
       "Create y Txn matrix from VAR model where `y[t,:] = A1*y[t-1,:] +...+Ap*y[t-p,:] + ϵ[t,:]`\n",
       "\n",
       "A is an `nxnxp` array with `cat(A1,A2,...,dims=3)` `y₀` is `pxn` initial values of y (for [t=-2;t=-1;t=0] for a VAR(3))\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@doc2 VARFilter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#using CodeTracking\n",
    "#println(@code_string VARFilter([1],[1],[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mThe impulse responses:\u001b[22m\u001b[39m\n",
      "\n",
      "period    ϵ1->y1    ϵ1->y2    ϵ2->y1    ϵ2->y2\n",
      "-2         0.000     0.000     0.000     0.000\n",
      "-1         0.000     0.000     0.000     0.000\n",
      "0          1.000     0.000     0.000     1.000\n",
      "1          0.500     0.100     0.200    -0.300\n",
      "2          0.270     0.020     0.040     0.110\n",
      "3          0.139     0.021     0.042    -0.029\n",
      "4          0.074     0.008     0.015     0.013\n",
      "5          0.038     0.005     0.010    -0.002\n",
      "6          0.020     0.002     0.005     0.002\n",
      "7          0.011     0.001     0.003    -0.000\n",
      "8          0.006     0.001     0.001     0.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A1 = [0.5 0.2;\n",
    "      0.1 -0.3]\n",
    "\n",
    "τ_max  = 11\n",
    "period = -2:(τ_max-3)       #-2,-1,0,1,...\n",
    "\n",
    "ϵ1      = zeros(τ_max,2)\n",
    "ϵ1[3,1] = 1                                  #shock to variable 1 in period=0\n",
    "IR_ϵ1   = VARFilter(ϵ1,A1,zeros(1,2))        #IR of both variables\n",
    "\n",
    "ϵ2      = zeros(τ_max,2)\n",
    "ϵ2[3,2] = 1                                  #shock to variable 2 in period=0\n",
    "IR_ϵ2   = VARFilter(ϵ2,A1,zeros(1,2))        #IR of both variables\n",
    "\n",
    "printblue(\"The impulse responses:\\n\")\n",
    "printmat(IR_ϵ1,IR_ϵ2;colNames=[\"ϵ1->y1\",\"ϵ1->y2\",\"ϵ2->y1\",\"ϵ2->y2\"],\n",
    "                     rowNames=period,cell00=\"period\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( period,IR_ϵ1,   #to traditional indices\n",
    "           label = [\"variable 1\" \"variable 2\"],\n",
    "           linecolor = [:red :blue],\n",
    "           linestyle = [:solid :dash],\n",
    "           xticks = period,\n",
    "           xlims = (0,8),       #period 0 and onwards\n",
    "           xlabel = \"period\",\n",
    "           title = \"IRF (shock to variable 1)\" )\n",
    "\n",
    "p2 = plot( period,IR_ϵ2,\n",
    "           label = [\"variable 1\" \"variable 2\"],\n",
    "           linecolor = [:red :blue],\n",
    "           linestyle = [:solid :dash],\n",
    "           xticks = period,\n",
    "           xlims = (0,8),\n",
    "           xlabel = \"period\",\n",
    "           title = \"IRF (shock to variable 2)\" )\n",
    "\n",
    "p = plot(p1,p2,layout=(1,2),size=(480*2,320))\n",
    "display(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forecasting with a VAR Process\n",
    "\n",
    "The cell below shows that forecasting with a VAR is very similar to forecasting with an AR: a simple recursive approach works well. However, for simplicity we will again use the `VARFilter()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "period        y1        y2\n",
      "-2         0.000     0.000\n",
      "-1         0.000     0.000\n",
      "0          1.000     2.000\n",
      "1          0.900    -0.500\n",
      "2          0.350     0.240\n",
      "3          0.223    -0.037\n",
      "4          0.104     0.033\n",
      "5          0.059     0.000\n",
      "6          0.029     0.006\n",
      "7          0.016     0.001\n",
      "8          0.008     0.001\n",
      "\n"
     ]
    }
   ],
   "source": [
    "τ_max  = 11\n",
    "period = -2:(τ_max-3)       #-2,-1,0,1,...\n",
    "\n",
    "y0 = [1 2]\n",
    "y2 = VARFilter(zeros(8,2),A1,y0)\n",
    "y2 = [zeros(2,2);y0;y2]                      #pad with initial values\n",
    "\n",
    "printmat(y2,colNames=[\"y1\",\"y2\"],rowNames=period,cell00=\"period\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( period,y2,\n",
    "           label = [\"variable 1\" \"variable 2\"],\n",
    "           linecolor = [:red :blue],\n",
    "           linestyle = [:solid :dash],\n",
    "           xticks = period,\n",
    "           xlims = (0,8),\n",
    "           xlabel = \"period\",\n",
    "           title = \"Forecast with VAR(1)\",\n",
    "           annotate=(1.3,1.8,text(\"y₀ = [1,2]\",8)) )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-Stationary Processes\n",
    "\n",
    "The cells below shows the impulse response function and the roots of a non-stationary AR(3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = [2.5,-2,0.5]                      #AR(3) coefficients\n",
    "\n",
    "τ_max  = 11\n",
    "period = -2:(τ_max-3)       #-2,-1,0,1,...\n",
    "\n",
    "ϵ    = zeros(τ_max)\n",
    "ϵ[3] = 1                     #a single shock, otherwise zeros\n",
    "\n",
    "y1 = ARMAFilter(ϵ,a)\n",
    "\n",
    "p1 = plot( period,y1,\n",
    "           label = \"\",\n",
    "           linecolor = :red,\n",
    "           xticks = period,\n",
    "           xlims = (0,8),\n",
    "           xlabel = \"period\",\n",
    "           title = \"Response to a shock in period 0\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "absolute values of the eigenvalues: should be < 1 for stationarity\n",
      "     0.500\n",
      "     1.000\n",
      "     1.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "λ = eigen(CompanionFormAR(a)).values    #eigenvalues of the companion form\n",
    "\n",
    "println(\"absolute values of the eigenvalues: should be < 1 for stationarity\")\n",
    "printmat(abs.(λ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 1.11.1",
   "language": "julia",
   "name": "julia-1.11"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
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