{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Covariance Stationary Processes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Covariance Stationary Processes](#Covariance-Stationary-Processes) \n", " - [Overview](#Overview) \n", " - [Introduction](#Introduction) \n", " - [Spectral Analysis](#Spectral-Analysis) \n", " - [Implementation](#Implementation) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "In this lecture we study covariance stationary linear stochastic processes, a\n", "class of models routinely used to study economic and financial time series.\n", "\n", "This class has the advantage of being\n", "\n", "1. simple enough to be described by an elegant and comprehensive theory \n", "1. relatively broad in terms of the kinds of dynamics it can represent \n", "\n", "\n", "We consider these models in both the time and frequency domain." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARMA Processes\n", "\n", "We will focus much of our attention on linear covariance stationary models with a finite number of parameters.\n", "\n", "In particular, we will study stationary ARMA processes, which form a cornerstone of the standard theory of time series analysis.\n", "\n", "Every ARMA processes can be represented in [linear state space](../tools_and_techniques/linear_models.html) form.\n", "\n", "However, ARMA have some important structure that makes it valuable to study them separately." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spectral Analysis\n", "\n", "Analysis in the frequency domain is also called spectral analysis.\n", "\n", "In essence, spectral analysis provides an alternative representation of the\n", "autocovariance function of a covariance stationary process.\n", "\n", "Having a second representation of this important object\n", "\n", "- shines light on the dynamics of the process in question \n", "- allows for a simpler, more tractable representation in some important cases \n", "\n", "\n", "The famous *Fourier transform* and its inverse are used to map between the two representations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Other Reading\n", "\n", "For supplementary reading, see.\n", "\n", "- [[LS18]](../zreferences.html#ljungqvist2012), chapter 2 \n", "- [[Sar87]](../zreferences.html#sargent1987), chapter 11 \n", "- John Cochrane’s notes on time series analysis, chapter 8 \n", "- [[Shi95]](../zreferences.html#shiryaev1995), chapter 6 \n", "- [[CC08]](../zreferences.html#cryerchan2008), all " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using InstantiateFromURL\n", "# optionally add arguments to force installation: instantiate = true, precompile = true\n", "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using LinearAlgebra, Statistics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "Consider a sequence of random variables $ \\{ X_t \\} $ indexed by $ t \\in \\mathbb Z $ and taking values in $ \\mathbb R $.\n", "\n", "Thus, $ \\{ X_t \\} $ begins in the infinite past and extends to the infinite future — a convenient and standard assumption.\n", "\n", "As in other fields, successful economic modeling typically assumes the existence of features that are constant over time.\n", "\n", "If these assumptions are correct, then each new observation $ X_t, X_{t+1},\\ldots $ can provide additional information about the time-invariant features, allowing us to learn from as data arrive.\n", "\n", "For this reason, we will focus in what follows on processes that are *stationary* — or become so after a transformation\n", "(see for example [this lecture](additive_functionals.html) and [this lecture](multiplicative_functionals.html)).\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Definitions\n", "\n", "\n", "\n", "A real-valued stochastic process $ \\{ X_t \\} $ is called *covariance stationary* if\n", "\n", "1. Its mean $ \\mu := \\mathbb E X_t $ does not depend on $ t $. \n", "1. For all $ k $ in $ \\mathbb Z $, the $ k $-th autocovariance $ \\gamma(k) := \\mathbb E (X_t - \\mu)(X_{t + k} - \\mu) $ is finite and depends only on $ k $. \n", "\n", "\n", "The function $ \\gamma \\colon \\mathbb Z \\to \\mathbb R $ is called the *autocovariance function* of the process.\n", "\n", "Throughout this lecture, we will work exclusively with zero-mean (i.e., $ \\mu = 0 $) covariance stationary processes.\n", "\n", "The zero-mean assumption costs nothing in terms of generality, since working with non-zero-mean processes involves no more than adding a constant." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 1: White Noise\n", "\n", "Perhaps the simplest class of covariance stationary processes is the white noise processes.\n", "\n", "A process $ \\{ \\epsilon_t \\} $ is called a *white noise process* if\n", "\n", "1. $ \\mathbb E \\epsilon_t = 0 $ \n", "1. $ \\gamma(k) = \\sigma^2 \\mathbf 1\\{k = 0\\} $ for some $ \\sigma > 0 $ \n", "\n", "\n", "(Here $ \\mathbf 1\\{k = 0\\} $ is defined to be 1 if $ k = 0 $ and zero otherwise)\n", "\n", "White noise processes play the role of **building blocks** for processes with more complicated dynamics.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 2: General Linear Processes\n", "\n", "From the simple building block provided by white noise, we can construct a very flexible family of covariance stationary processes — the *general linear processes*\n", "\n", "\n", "\n", "$$\n", "X_t = \\sum_{j=0}^{\\infty} \\psi_j \\epsilon_{t-j},\n", "\\qquad t \\in \\mathbb Z \\tag{1}\n", "$$\n", "\n", "where\n", "\n", "- $ \\{\\epsilon_t\\} $ is white noise \n", "- $ \\{\\psi_t\\} $ is a square summable sequence in $ \\mathbb R $ (that is, $ \\sum_{t=0}^{\\infty} \\psi_t^2 < \\infty $) \n", "\n", "\n", "The sequence $ \\{\\psi_t\\} $ is often called a *linear filter*.\n", "\n", "Equation [(1)](#equation-ma-inf) is said to present a **moving average** process or a moving average representation.\n", "\n", "With some manipulations it is possible to confirm that the autocovariance function for [(1)](#equation-ma-inf) is\n", "\n", "\n", "\n", "$$\n", "\\gamma(k) = \\sigma^2 \\sum_{j=0}^{\\infty} \\psi_j \\psi_{j+k} \\tag{2}\n", "$$\n", "\n", "By the [Cauchy-Schwartz inequality](https://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality) one can show that $ \\gamma(k) $ satisfies equation [(2)](#equation-ma-inf-ac).\n", "\n", "Evidently, $ \\gamma(k) $ does not depend on $ t $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Wold’s Decomposition\n", "\n", "Remarkably, the class of general linear processes goes a long way towards\n", "describing the entire class of zero-mean covariance stationary processes.\n", "\n", "In particular, [Wold’s decomposition theorem](https://en.wikipedia.org/wiki/Wold%27s_theorem) states that every\n", "zero-mean covariance stationary process $ \\{X_t\\} $ can be written as\n", "\n", "$$\n", "X_t = \\sum_{j=0}^{\\infty} \\psi_j \\epsilon_{t-j} + \\eta_t\n", "$$\n", "\n", "where\n", "\n", "- $ \\{\\epsilon_t\\} $ is white noise \n", "- $ \\{\\psi_t\\} $ is square summable \n", "- $ \\eta_t $ can be expressed as a linear function of $ X_{t-1}, X_{t-2},\\ldots $ and is perfectly predictable over arbitrarily long horizons \n", "\n", "\n", "For intuition and further discussion, see [[Sar87]](../zreferences.html#sargent1987), p. 286." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### AR and MA\n", "\n", "\n", "\n", "General linear processes are a very broad class of processes.\n", "\n", "It often pays to specialize to those for which there exists a representation having only finitely many parameters.\n", "\n", "(Experience and theory combine to indicate that models with a relatively small number of parameters typically perform better than larger models, especially for forecasting)\n", "\n", "One very simple example of such a model is the first-order autoregressive or AR(1) process\n", "\n", "\n", "\n", "$$\n", "X_t = \\phi X_{t-1} + \\epsilon_t\n", "\\quad \\text{where} \\quad\n", "| \\phi | < 1\n", "\\quad \\text{and } \\{ \\epsilon_t \\} \\text{ is white noise} \\tag{3}\n", "$$\n", "\n", "By direct substitution, it is easy to verify that $ X_t = \\sum_{j=0}^{\\infty} \\phi^j \\epsilon_{t-j} $.\n", "\n", "Hence $ \\{X_t\\} $ is a general linear process.\n", "\n", "Applying [(2)](#equation-ma-inf-ac) to the previous expression for $ X_t $, we get the AR(1) autocovariance function\n", "\n", "\n", "\n", "$$\n", "\\gamma(k) = \\phi^k \\frac{\\sigma^2}{1 - \\phi^2},\n", "\\qquad k = 0, 1, \\ldots \\tag{4}\n", "$$\n", "\n", "The next figure plots an example of this function for $ \\phi = 0.8 $ and $ \\phi = -0.8 $ with $ \\sigma = 1 $" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots\n", "gr(fmt=:png);\n", "\n", "plt_1=plot()\n", "plt_2=plot()\n", "plots = [plt_1, plt_2]\n", "\n", "for (i, ϕ) in enumerate((0.8, -0.8))\n", " times = 0:16\n", " acov = [ϕ.^k ./ (1 - ϕ.^2) for k in times]\n", " label = \"autocovariance, phi = $ϕ\"\n", " plot!(plots[i], times, acov, color=:blue, lw=2, marker=:circle, markersize=3,\n", " alpha=0.6, label=label)\n", " plot!(plots[i], legend=:topright, xlabel=\"time\", xlim=(0,15))\n", " plot!(plots[i], seriestype=:hline, [0], linestyle=:dash, alpha=0.5, lw=2, label=\"\")\n", "end\n", "plot(plots[1], plots[2], layout=(2,1), size=(700,500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another very simple process is the MA(1) process (here MA means “moving average”)\n", "\n", "$$\n", "X_t = \\epsilon_t + \\theta \\epsilon_{t-1}\n", "$$\n", "\n", "You will be able to verify that\n", "\n", "$$\n", "\\gamma(0) = \\sigma^2 (1 + \\theta^2),\n", "\\quad\n", "\\gamma(1) = \\sigma^2 \\theta,\n", "\\quad \\text{and} \\quad\n", "\\gamma(k) = 0 \\quad \\forall \\, k > 1\n", "$$\n", "\n", "The AR(1) can be generalized to an AR($ p $) and likewise for the MA(1).\n", "\n", "Putting all of this together, we get the" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARMA Processes\n", "\n", "A stochastic process $ \\{X_t\\} $ is called an *autoregressive moving\n", "average process*, or ARMA($ p,q $), if it can be written as\n", "\n", "\n", "\n", "$$\n", "X_t = \\phi_1 X_{t-1} + \\cdots + \\phi_p X_{t-p} +\n", " \\epsilon_t + \\theta_1 \\epsilon_{t-1} + \\cdots + \\theta_q \\epsilon_{t-q} \\tag{5}\n", "$$\n", "\n", "where $ \\{ \\epsilon_t \\} $ is white noise.\n", "\n", "An alternative notation for ARMA processes uses the *lag operator* $ L $.\n", "\n", "**Def.** Given arbitrary variable $ Y_t $, let $ L^k Y_t := Y_{t-k} $.\n", "\n", "It turns out that\n", "\n", "- lag operators facilitate succinct representations for linear stochastic processes \n", "- algebraic manipulations that treat the lag operator as an ordinary scalar are legitimate \n", "\n", "\n", "Using $ L $, we can rewrite [(5)](#equation-arma) as\n", "\n", "\n", "\n", "$$\n", "L^0 X_t - \\phi_1 L^1 X_t - \\cdots - \\phi_p L^p X_t = L^0 \\epsilon_t + \\theta_1 L^1 \\epsilon_t + \\cdots + \\theta_q L^q \\epsilon_t \\tag{6}\n", "$$\n", "\n", "If we let $ \\phi(z) $ and $ \\theta(z) $ be the polynomials\n", "\n", "\n", "\n", "$$\n", "\\phi(z) := 1 - \\phi_1 z - \\cdots - \\phi_p z^p\n", "\\quad \\text{and} \\quad\n", "\\theta(z) := 1 + \\theta_1 z + \\cdots + \\theta_q z^q \\tag{7}\n", "$$\n", "\n", "then [(6)](#equation-arma-lag) becomes\n", "\n", "\n", "\n", "$$\n", "\\phi(L) X_t = \\theta(L) \\epsilon_t \\tag{8}\n", "$$\n", "\n", "In what follows we **always assume** that the roots of the polynomial $ \\phi(z) $ lie outside the unit circle in the complex plane.\n", "\n", "This condition is sufficient to guarantee that the ARMA($ p,q $) process is convariance stationary.\n", "\n", "In fact it implies that the process falls within the class of general linear processes [described above](#generalized-lps).\n", "\n", "That is, given an ARMA($ p,q $) process $ \\{ X_t \\} $ satisfying the unit circle condition, there exists a square summable sequence $ \\{\\psi_t\\} $ with $ X_t = \\sum_{j=0}^{\\infty} \\psi_j \\epsilon_{t-j} $ for all $ t $.\n", "\n", "The sequence $ \\{\\psi_t\\} $ can be obtained by a recursive procedure outlined on page 79 of [[CC08]](../zreferences.html#cryerchan2008).\n", "\n", "The function $ t \\mapsto \\psi_t $ is often called the *impulse response function*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spectral Analysis\n", "\n", "Autocovariance functions provide a great deal of information about covariance stationary processes.\n", "\n", "In fact, for zero-mean Gaussian processes, the autocovariance function characterizes the entire joint distribution.\n", "\n", "Even for non-Gaussian processes, it provides a significant amount of information.\n", "\n", "It turns out that there is an alternative representation of the autocovariance function of a covariance stationary process, called the *spectral density*.\n", "\n", "At times, the spectral density is easier to derive, easier to manipulate, and provides additional intuition." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Complex Numbers\n", "\n", "Before discussing the spectral density, we invite you to recall the main properties of complex numbers (or [skip to the next section](#arma-specd)).\n", "\n", "It can be helpful to remember that, in a formal sense, complex numbers are just points $ (x, y) \\in \\mathbb R^2 $ endowed with a specific notion of multiplication.\n", "\n", "When $ (x, y) $ is regarded as a complex number, $ x $ is called the *real part* and $ y $ is called the *imaginary part*.\n", "\n", "The *modulus* or *absolute value* of a complex number $ z = (x, y) $ is just its Euclidean norm in $ \\mathbb R^2 $, but is usually written as $ |z| $ instead of $ \\|z\\| $.\n", "\n", "The product of two complex numbers $ (x, y) $ and $ (u, v) $ is defined to be $ (xu - vy, xv + yu) $, while addition is standard pointwise vector addition.\n", "\n", "When endowed with these notions of multiplication and addition, the set of complex numbers forms a [field](https://en.wikipedia.org/wiki/Field_%28mathematics%29) — addition and multiplication play well together, just as they do in $ \\mathbb R $.\n", "\n", "The complex number $ (x, y) $ is often written as $ x + i y $, where $ i $ is called the *imaginary unit*, and is understood to obey $ i^2 = -1 $.\n", "\n", "The $ x + i y $ notation provides an easy way to remember the definition of multiplication given above, because, proceeding naively,\n", "\n", "$$\n", "(x + i y) (u + i v) = xu - yv + i (xv + yu)\n", "$$\n", "\n", "Converted back to our first notation, this becomes $ (xu - vy, xv + yu) $ as promised.\n", "\n", "Complex numbers can be represented in the polar form $ r e^{i \\omega} $ where\n", "\n", "$$\n", "r e^{i \\omega} := r (\\cos(\\omega) + i \\sin(\\omega)) = x + i y\n", "$$\n", "\n", "where $ x = r \\cos(\\omega), y = r \\sin(\\omega) $, and $ \\omega = \\arctan(y/z) $ or $ \\tan(\\omega) = y/x $.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spectral Densities\n", "\n", "Let $ \\{ X_t \\} $ be a covariance stationary process with autocovariance function $ \\gamma $ satisfying $ \\sum_{k} \\gamma(k)^2 < \\infty $.\n", "\n", "The *spectral density* $ f $ of $ \\{ X_t \\} $ is defined as the [discrete time Fourier transform](https://en.wikipedia.org/wiki/Discrete-time_Fourier_transform) of its autocovariance function $ \\gamma $\n", "\n", "$$\n", "f(\\omega) := \\sum_{k \\in \\mathbb Z} \\gamma(k) e^{-i \\omega k},\n", "\\qquad \\omega \\in \\mathbb R\n", "$$\n", "\n", "(Some authors normalize the expression on the right by constants such as $ 1/\\pi $ — the convention chosen makes little difference provided you are consistent)\n", "\n", "Using the fact that $ \\gamma $ is *even*, in the sense that $ \\gamma(t) = \\gamma(-t) $ for all $ t $, we can show that\n", "\n", "\n", "\n", "$$\n", "f(\\omega) = \\gamma(0) + 2 \\sum_{k \\geq 1} \\gamma(k) \\cos(\\omega k) \\tag{9}\n", "$$\n", "\n", "It is not difficult to confirm that $ f $ is\n", "\n", "- real-valued \n", "- even ($ f(\\omega) = f(-\\omega) $ ), and \n", "- $ 2\\pi $-periodic, in the sense that $ f(2\\pi + \\omega) = f(\\omega) $ for all $ \\omega $ \n", "\n", "\n", "It follows that the values of $ f $ on $ [0, \\pi] $ determine the values of $ f $ on\n", "all of $ \\mathbb R $ — the proof is an exercise.\n", "\n", "For this reason it is standard to plot the spectral density only on the interval $ [0, \\pi] $.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 1: White Noise\n", "\n", "Consider a white noise process $ \\{\\epsilon_t\\} $ with standard deviation $ \\sigma $.\n", "\n", "It is easy to check that in this case $ f(\\omega) = \\sigma^2 $. So $ f $ is a constant function.\n", "\n", "As we will see, this can be interpreted as meaning that “all frequencies are equally present”.\n", "\n", "(White light has this property when frequency refers to the visible spectrum, a connection that provides the origins of the term “white noise”)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 2: AR and MA and ARMA\n", "\n", "\n", "\n", "It is an exercise to show that the MA(1) process $ X_t = \\theta \\epsilon_{t-1} + \\epsilon_t $ has spectral density\n", "\n", "\n", "\n", "$$\n", "f(\\omega)\n", "= \\sigma^2 ( 1 + 2 \\theta \\cos(\\omega) + \\theta^2 ) \\tag{10}\n", "$$\n", "\n", "With a bit more effort, it is possible to show (see, e.g., p. 261 of [[Sar87]](../zreferences.html#sargent1987)) that the spectral density of the AR(1) process $ X_t = \\phi X_{t-1} + \\epsilon_t $ is\n", "\n", "\n", "\n", "$$\n", "f(\\omega)\n", "= \\frac{\\sigma^2}{ 1 - 2 \\phi \\cos(\\omega) + \\phi^2 } \\tag{11}\n", "$$\n", "\n", "More generally, it can be shown that the spectral density of the ARMA process [(5)](#equation-arma) is\n", "\n", "\n", "\n", "\n", "\n", "$$\n", "f(\\omega) = \\left| \\frac{\\theta(e^{i\\omega})}{\\phi(e^{i\\omega})} \\right|^2 \\sigma^2 \\tag{12}\n", "$$\n", "\n", "where\n", "\n", "- $ \\sigma $ is the standard deviation of the white noise process $ \\{\\epsilon_t\\} $ \n", "- the polynomials $ \\phi(\\cdot) $ and $ \\theta(\\cdot) $ are as defined in [(7)](#equation-arma-poly) \n", "\n", "\n", "The derivation of [(12)](#equation-arma-sd) uses the fact that convolutions become products under Fourier transformations.\n", "\n", "The proof is elegant and can be found in many places — see, for example, [[Sar87]](../zreferences.html#sargent1987), chapter 11, section 4.\n", "\n", "It is a nice exercise to verify that [(10)](#equation-ma1-sd-ed) and [(11)](#equation-ar1-sd-ed) are indeed special cases of [(12)](#equation-arma-sd)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interpreting the Spectral Density\n", "\n", "\n", "\n", "Plotting [(11)](#equation-ar1-sd-ed) reveals the shape of the spectral density for the AR(1) model when $ \\phi $ takes the values 0.8 and -0.8 respectively" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ar1_sd(ϕ, ω) = 1 ./ (1 .- 2 * ϕ * cos.(ω) .+ ϕ.^2)\n", "\n", "ω_s = range(0, π, length = 180)\n", "\n", "plt_1=plot()\n", "plt_2=plot()\n", "plots=[plt_1, plt_2]\n", "\n", "for (i, ϕ) in enumerate((0.8, -0.8))\n", " sd = ar1_sd(ϕ, ω_s)\n", " label = \"spectral density, phi = $ϕ\"\n", " plot!(plots[i], ω_s, sd, color=:blue, alpha=0.6, lw=2, label=label)\n", " plot!(plots[i], legend=:top, xlabel=\"frequency\", xlim=(0,π))\n", "end\n", "plot(plots[1], plots[2], layout=(2,1), size=(700,500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These spectral densities correspond to the autocovariance functions for the\n", "AR(1) process [shown above](#ar1-acov).\n", "\n", "Informally, we think of the spectral density as being large at those $ \\omega \\in [0, \\pi] $ at which\n", "the autocovariance function seems approximately to exhibit big damped cycles.\n", "\n", "To see the idea, let’s consider why, in the lower panel of the preceding figure, the spectral density for the case $ \\phi = -0.8 $ is large at $ \\omega = \\pi $.\n", "\n", "Recall that the spectral density can be expressed as\n", "\n", "\n", "\n", "$$\n", "f(\\omega)\n", "= \\gamma(0) + 2 \\sum_{k \\geq 1} \\gamma(k) \\cos(\\omega k)\n", "= \\gamma(0) + 2 \\sum_{k \\geq 1} (-0.8)^k \\cos(\\omega k) \\tag{13}\n", "$$\n", "\n", "When we evaluate this at $ \\omega = \\pi $, we get a large number because\n", "$ \\cos(\\pi k) $ is large and positive when $ (-0.8)^k $ is\n", "positive, and large in absolute value and negative when $ (-0.8)^k $ is negative.\n", "\n", "Hence the product is always large and positive, and hence the sum of the\n", "products on the right-hand side of [(13)](#equation-sumpr) is large.\n", "\n", "These ideas are illustrated in the next figure, which has $ k $ on the horizontal axis" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ϕ = -0.8\n", "times = 0:16\n", "y1 = [ϕ.^k ./ (1 - ϕ.^2) for k in times]\n", "y2 = [cos.(π * k) for k in times]\n", "y3 = [a * b for (a, b) in zip(y1, y2)]\n", "\n", "# Autocovariance when ϕ = -0.8\n", "plt_1 = plot(times, y1, color=:blue, lw=2, marker=:circle, markersize=3,\n", " alpha=0.6, label=\"gamma(k)\")\n", "plot!(plt_1, seriestype=:hline, [0], linestyle=:dash, alpha=0.5,\n", " lw=2, label=\"\")\n", "plot!(plt_1, legend=:topright, xlim=(0,15), yticks=[-2, 0, 2])\n", "\n", "# Cycles at frequence π\n", "plt_2 = plot(times, y2, color=:blue, lw=2, marker=:circle, markersize=3,\n", " alpha=0.6, label=\"cos(pi k)\")\n", "plot!(plt_2, seriestype=:hline, [0], linestyle=:dash, alpha=0.5,\n", " lw=2, label=\"\")\n", "plot!(plt_2, legend=:topright, xlim=(0,15), yticks=[-1, 0, 1])\n", "\n", "# Product\n", "plt_3 = plot(times, y3, seriestype=:sticks, marker=:circle, markersize=3,\n", " lw=2, label=\"gamma(k) cos(pi k)\")\n", "plot!(plt_3, seriestype=:hline, [0], linestyle=:dash, alpha=0.5,\n", " lw=2, label=\"\")\n", "plot!(plt_3, legend=:topright, xlim=(0,15), ylim=(-3,3), yticks=[-1, 0, 1, 2, 3])\n", "\n", "plot(plt_1, plt_2, plt_3, layout=(3,1), size=(800,600))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the other hand, if we evaluate $ f(\\omega) $ at $ \\omega = \\pi / 3 $, then the cycles are\n", "not matched, the sequence $ \\gamma(k) \\cos(\\omega k) $ contains\n", "both positive and negative terms, and hence the sum of these terms is much smaller" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ϕ = -0.8\n", "times = 0:16\n", "y1 = [ϕ.^k ./ (1 - ϕ.^2) for k in times]\n", "y2 = [cos.(π * k/3) for k in times]\n", "y3 = [a * b for (a, b) in zip(y1, y2)]\n", "\n", "# Autocovariance when ϕ = -0.8\n", "plt_1 = plot(times, y1, color=:blue, lw=2, marker=:circle, markersize=3,\n", " alpha=0.6, label=\"gamma(k)\")\n", "plot!(plt_1, seriestype=:hline, [0], linestyle=:dash, alpha=0.5,\n", " lw=2, label=\"\")\n", "plot!(plt_1, legend=:topright, xlim=(0,15), yticks=[-2, 0, 2])\n", "\n", "# Cycles at frequence π\n", "plt_2 = plot(times, y2, color=:blue, lw=2, marker=:circle, markersize=3,\n", " alpha=0.6, label=\"cos(pi k/3)\")\n", "plot!(plt_2, seriestype=:hline, [0], linestyle=:dash, alpha=0.5,\n", " lw=2, label=\"\")\n", "plot!(plt_2, legend=:topright, xlim=(0,15), yticks=[-1, 0, 1])\n", "\n", "# Product\n", "plt_3 = plot(times, y3, seriestype=:sticks, marker=:circle, markersize=3,\n", " lw=2, label=\"gamma(k) cos(pi k/3)\")\n", "plot!(plt_3, seriestype=:hline, [0], linestyle=:dash, alpha=0.5,\n", " lw=2, label=\"\")\n", "plot!(plt_3, legend=:topright, xlim=(0,15), ylim=(-3,3), yticks=[-1, 0, 1, 2, 3])\n", "\n", "plot(plt_1, plt_2, plt_3, layout=(3,1), size=(600,600))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In summary, the spectral density is large at frequencies $ \\omega $ where the autocovariance function exhibits damped cycles." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Inverting the Transformation\n", "\n", "\n", "\n", "We have just seen that the spectral density is useful in the sense that it provides a frequency-based perspective on the autocovariance structure of a covariance stationary process.\n", "\n", "Another reason that the spectral density is useful is that it can be “inverted” to recover the autocovariance function via the *inverse Fourier transform*.\n", "\n", "In particular, for all $ k \\in \\mathbb Z $, we have\n", "\n", "\n", "\n", "$$\n", "\\gamma(k) = \\frac{1}{2 \\pi} \\int_{-\\pi}^{\\pi} f(\\omega) e^{i \\omega k} d\\omega \\tag{14}\n", "$$\n", "\n", "This is convenient in situations where the spectral density is easier to calculate and manipulate than the autocovariance function.\n", "\n", "(For example, the expression [(12)](#equation-arma-sd) for the ARMA spectral density is much easier to work with than the expression for the ARMA autocovariance)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mathematical Theory\n", "\n", "\n", "\n", "This section is loosely based on [[Sar87]](../zreferences.html#sargent1987), p. 249-253, and included for those who\n", "\n", "- would like a bit more insight into spectral densities \n", "- and have at least some background in [Hilbert space](https://en.wikipedia.org/wiki/Hilbert_space) theory \n", "\n", "\n", "Others should feel free to skip to the [next section](#arma-imp) — none of this material is necessary to progress to computation.\n", "\n", "Recall that every [separable](https://en.wikipedia.org/wiki/Separable_space) Hilbert space $ H $ has a countable orthonormal basis $ \\{ h_k \\} $.\n", "\n", "The nice thing about such a basis is that every $ f \\in H $ satisfies\n", "\n", "\n", "\n", "$$\n", "f = \\sum_k \\alpha_k h_k\n", "\\quad \\text{where} \\quad\n", "\\alpha_k := \\langle f, h_k \\rangle \\tag{15}\n", "$$\n", "\n", "where $ \\langle \\cdot, \\cdot \\rangle $ denotes the inner product in $ H $.\n", "\n", "Thus, $ f $ can be represented to any degree of precision by linearly combining basis vectors.\n", "\n", "The scalar sequence $ \\alpha = \\{\\alpha_k\\} $ is called the *Fourier coefficients* of $ f $, and satisfies $ \\sum_k |\\alpha_k|^2 < \\infty $.\n", "\n", "In other words, $ \\alpha $ is in $ \\ell_2 $, the set of square summable sequences.\n", "\n", "Consider an operator $ T $ that maps $ \\alpha \\in \\ell_2 $ into its expansion $ \\sum_k \\alpha_k h_k \\in H $.\n", "\n", "The Fourier coefficients of $ T\\alpha $ are just $ \\alpha = \\{ \\alpha_k \\} $, as you can verify by confirming that $ \\langle T \\alpha, h_k \\rangle = \\alpha_k $.\n", "\n", "Using elementary results from Hilbert space theory, it can be shown that\n", "\n", "- $ T $ is one-to-one — if $ \\alpha $ and $ \\beta $ are distinct in $ \\ell_2 $, then so are their expansions in $ H $ \n", "- $ T $ is onto — if $ f \\in H $ then its preimage in $ \\ell_2 $ is the sequence $ \\alpha $ given by $ \\alpha_k = \\langle f, h_k \\rangle $ \n", "- $ T $ is a linear isometry — in particular $ \\langle \\alpha, \\beta \\rangle = \\langle T\\alpha, T\\beta \\rangle $ \n", "\n", "\n", "Summarizing these results, we say that any separable Hilbert space is isometrically isomorphic to $ \\ell_2 $.\n", "\n", "In essence, this says that each separable Hilbert space we consider is just a different way of looking at the fundamental space $ \\ell_2 $.\n", "\n", "With this in mind, let’s specialize to a setting where\n", "\n", "- $ \\gamma \\in \\ell_2 $ is the autocovariance function of a covariance stationary process, and $ f $ is the spectral density \n", "- $ H = L_2 $, where $ L_2 $ is the set of square summable functions on the interval $ [-\\pi, \\pi] $, with inner product $ \\langle g, h \\rangle = \\int_{-\\pi}^{\\pi} g(\\omega) h(\\omega) d \\omega $ \n", "- $ \\{h_k\\} = $ the orthonormal basis for $ L_2 $ given by the set of trigonometric functions \n", "\n", "\n", "$$\n", "h_k(\\omega) = \\frac{e^{i \\omega k}}{\\sqrt{2 \\pi}},\n", "\\quad k \\in \\mathbb Z,\n", "\\quad \\omega \\in [-\\pi, \\pi]\n", "$$\n", "\n", "Using the definition of $ T $ from above and the fact that $ f $ is even, we now have\n", "\n", "\n", "\n", "$$\n", "T \\gamma\n", "= \\sum_{k \\in \\mathbb Z}\n", "\\gamma(k) \\frac{e^{i \\omega k}}{\\sqrt{2 \\pi}} = \\frac{1}{\\sqrt{2 \\pi}} f(\\omega) \\tag{16}\n", "$$\n", "\n", "In other words, apart from a scalar multiple, the spectral density is just an transformation of $ \\gamma \\in \\ell_2 $ under a certain linear isometry — a different way to view $ \\gamma $.\n", "\n", "In particular, it is an expansion of the autocovariance function with respect to the trigonometric basis functions in $ L_2 $.\n", "\n", "As discussed above, the Fourier coefficients of $ T \\gamma $ are given by the sequence $ \\gamma $, and,\n", "in particular, $ \\gamma(k) = \\langle T \\gamma, h_k \\rangle $.\n", "\n", "Transforming this inner product into its integral expression and using [(16)](#equation-arma-it) gives\n", "[(14)](#equation-ift), justifying our earlier expression for the inverse transform.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "Most code for working with covariance stationary models deals with ARMA models.\n", "\n", "Julia code for studying ARMA models can be found in the `DSP.jl` package.\n", "\n", "Since this code doesn’t quite cover our needs — particularly vis-a-vis spectral analysis — we’ve put together the module [arma.jl](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/arma.jl), which is part of [QuantEcon.jl](http://quantecon.org/quantecon-jl) package.\n", "\n", "The module provides functions for mapping ARMA($ p,q $) models into their\n", "\n", "1. impulse response function \n", "1. simulated time series \n", "1. autocovariance function \n", "1. spectral density " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Application\n", "\n", "Let’s use this code to replicate the plots on pages 68–69 of [[LS18]](../zreferences.html#ljungqvist2012).\n", "\n", "Here are some functions to generate the plots" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "quad_plot (generic function with 1 method)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using QuantEcon, Random\n", "\n", "# plot functions\n", "function plot_spectral_density(arma, plt)\n", " (w, spect) = spectral_density(arma, two_pi=false)\n", " plot!(plt, w, spect, lw=2, alpha=0.7,label=\"\")\n", " plot!(plt, title=\"Spectral density\", xlim=(0,π),\n", " xlabel=\"frequency\", ylabel=\"spectrum\", yscale=:log)\n", " return plt\n", "end\n", "\n", "function plot_spectral_density(arma)\n", " plt = plot()\n", " plot_spectral_density(arma, plt=plt)\n", " return plt\n", "end\n", "\n", "function plot_autocovariance(arma, plt)\n", " acov = autocovariance(arma)\n", " n = length(acov)\n", " plot!(plt, 0:(n-1), acov, seriestype=:sticks, marker=:circle,\n", " markersize=2,label=\"\")\n", " plot!(plt, seriestype=:hline, [0], color=:red, label=\"\")\n", " plot!(plt, title=\"Autocovariance\", xlim=(-0.5, n-0.5),\n", " xlabel=\"time\", ylabel=\"autocovariance\")\n", " return plt\n", "end\n", "\n", "function plot_autocovariance(arma)\n", " plt = plot()\n", " plot_spectral_density(arma, plt=plt)\n", " return plt\n", "end\n", "\n", "function plot_impulse_response(arma, plt)\n", " psi = impulse_response(arma)\n", " n = length(psi)\n", " plot!(plt, 0:(n-1), psi, seriestype=:sticks, marker=:circle,\n", " markersize=2, label=\"\")\n", " plot!(plt, seriestype=:hline, [0], color=:red, label=\"\")\n", " plot!(plt, title=\"Impluse response\", xlim=(-0.5,n-0.5),\n", " xlabel=\"time\", ylabel=\"response\")\n", " return plt\n", "end\n", "\n", "function plot_impulse_response(arma)\n", " plt = plot()\n", " plot_spectral_density(arma, plt=plt)\n", " return plt\n", "end\n", "\n", "function plot_simulation(arma, plt)\n", " X = simulation(arma)\n", " n = length(X)\n", " plot!(plt, 0:(n-1), X, lw=2, alpha=0.7, label=\"\")\n", " plot!(plt, title=\"Sample path\", xlim=(0,0,n), xlabel=\"time\", ylabel=\"state space\")\n", " return plt\n", "end\n", "\n", "function plot_simulation(arma)\n", " plt = plot()\n", " plot_spectral_density(arma, plt=plt)\n", " return plt\n", "end\n", "\n", "function quad_plot(arma)\n", " plt_1 = plot()\n", " plt_2 = plot()\n", " plt_3 = plot()\n", " plt_4 = plot()\n", " plots = [plt_1, plt_2, plt_3, plt_4]\n", "\n", " plot_functions = [plot_spectral_density,\n", " plot_impulse_response,\n", " plot_autocovariance,\n", " plot_simulation]\n", " for (i, plt, plot_func) in zip(1:1:4, plots, plot_functions)\n", " plots[i] = plot_func(arma, plt)\n", " end\n", " return plot(plots[1], plots[2], plots[3], plots[4], layout=(2,2), size=(800,800))\n", "\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let’s call these functions to generate the plots.\n", "\n", "We’ll use the model $ X_t = 0.5 X_{t-1} + \\epsilon_t - 0.8 \\epsilon_{t-2} $" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Random.seed!(42) # For reproducible results.\n", "ϕ = 0.5;\n", "θ = [0, -0.8];\n", "arma = ARMA(ϕ, θ, 1.0)\n", "quad_plot(arma)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Explanation\n", "\n", "The call" ] }, { "cell_type": "markdown", "metadata": { "hide-output": false }, "source": [ "```julia\n", "arma = ARMA(ϕ, θ, σ)\n", "```\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "creates an instance `arma` that represents the ARMA($ p, q $) model\n", "\n", "$$\n", "X_t = \\phi_1 X_{t-1} + ... + \\phi_p X_{t-p} +\n", " \\epsilon_t + \\theta_1 \\epsilon_{t-1} + ... + \\theta_q \\epsilon_{t-q}\n", "$$\n", "\n", "If `ϕ` and `θ` are arrays or sequences, then the interpretation will\n", "be\n", "\n", "- `ϕ` holds the vector of parameters $ (\\phi_1, \\phi_2,..., \\phi_p) $ \n", "- `θ` holds the vector of parameters $ (\\theta_1, \\theta_2,..., \\theta_q) $ \n", "\n", "\n", "The parameter `σ` is always a scalar, the standard deviation of the white noise.\n", "\n", "We also permit `ϕ` and `θ` to be scalars, in which case the model will be interpreted as\n", "\n", "$$\n", "X_t = \\phi X_{t-1} + \\epsilon_t + \\theta \\epsilon_{t-1}\n", "$$\n", "\n", "The two numerical packages most useful for working with ARMA models are `DSP.jl` and the `fft` routine in Julia." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing the Autocovariance Function\n", "\n", "As discussed above, for ARMA processes the spectral density has a [simple representation](#arma-spec-den) that is relatively easy to calculate.\n", "\n", "Given this fact, the easiest way to obtain the autocovariance function is to recover it from the spectral\n", "density via the inverse Fourier transform.\n", "\n", "Here we use Julia’s Fourier transform routine fft, which wraps a standard C-based package called FFTW.\n", "\n", "A look at [the fft documentation](https://docs.julialang.org/en/stable/stdlib/math/#Base.DFT.fft) shows that the inverse transform ifft takes a given sequence $ A_0, A_1, \\ldots, A_{n-1} $ and\n", "returns the sequence $ a_0, a_1, \\ldots, a_{n-1} $ defined by\n", "\n", "$$\n", "a_k = \\frac{1}{n} \\sum_{t=0}^{n-1} A_t e^{ik 2\\pi t / n}\n", "$$\n", "\n", "Thus, if we set $ A_t = f(\\omega_t) $, where $ f $ is the spectral density and\n", "$ \\omega_t := 2 \\pi t / n $, then\n", "\n", "$$\n", "a_k\n", "= \\frac{1}{n} \\sum_{t=0}^{n-1} f(\\omega_t) e^{i \\omega_t k}\n", "= \\frac{1}{2\\pi} \\frac{2 \\pi}{n} \\sum_{t=0}^{n-1} f(\\omega_t) e^{i \\omega_t k},\n", "\\qquad\n", "\\omega_t := 2 \\pi t / n\n", "$$\n", "\n", "For $ n $ sufficiently large, we then have\n", "\n", "$$\n", "a_k\n", "\\approx \\frac{1}{2\\pi} \\int_0^{2 \\pi} f(\\omega) e^{i \\omega k} d \\omega\n", "= \\frac{1}{2\\pi} \\int_{-\\pi}^{\\pi} f(\\omega) e^{i \\omega k} d \\omega\n", "$$\n", "\n", "(You can check the last equality)\n", "\n", "In view of [(14)](#equation-ift) we have now shown that, for $ n $ sufficiently large, $ a_k \\approx \\gamma(k) $ — which is exactly what we want to compute." ] } ], "metadata": { "date": 1591310626.534061, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "arma.rst", "filename_with_path": "time_series_models/arma", "kernelspec": { "display_name": "Julia 1.4.2", "language": "julia", "name": "julia-1.4" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.4.2" }, "title": "Covariance Stationary Processes" }, "nbformat": 4, "nbformat_minor": 2 }