{ "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](https://lectures.quantecon.org/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]](https://lectures.quantecon.org/zreferences.html#ljungqvist2012), chapter 2 \n", "- [[Sar87]](https://lectures.quantecon.org/zreferences.html#sargent1987), chapter 11 \n", "- John Cochrane’s notes on time series analysis, chapter 8 \n", "- [[Shi95]](https://lectures.quantecon.org/zreferences.html#shiryaev1995), chapter 6 \n", "- [[CC08]](https://lectures.quantecon.org/zreferences.html#cryerchan2008), all " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[32m\u001b[1mActivated\u001b[0m /home/qebuild/repos/lecture-source-jl/_build/website/jupyter/Project.toml\u001b[39m\n", "\u001b[36m\u001b[1mInfo\u001b[0m quantecon-notebooks-julia 0.1.0 activated, 0.2.0 requested\u001b[39m\n" ] } ], "source": [ "using InstantiateFromURL\n", "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.2.0\")" ] }, { "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](https://lectures.quantecon.org/additive_functionals.html) and [this lecture](https://lectures.quantecon.org/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]](https://lectures.quantecon.org/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]](https://lectures.quantecon.org/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]](https://lectures.quantecon.org/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]](https://lectures.quantecon.org/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]](https://lectures.quantecon.org/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 $\n", "\n", "Transforming this inner product into its integral expression and using [(16)](#equation-arma-it) gives\n", "[(14)](#equation-ift), justifying our earlier expression for the inverse transform\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "Most code for working with covariance stationary models deals with ARMA models\n", "\n", "Julia code for studying ARMA models can be found in the `DSP.jl` package\n", "\n", "Since this code doesn’t quite cover our needs — particularly vis-a-vis spectral analysis — we’ve put together the module [arma.jl](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/arma.jl), which is part of [QuantEcon.jl](http://quantecon.org/julia_index.html) package\n", "\n", "The module provides functions for mapping ARMA($ 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]](https://lectures.quantecon.org/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": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: DSP.TFFilter is deprecated, use PolynomialRatio instead.\n", " likely near /home/qebuild/.julia/packages/IJulia/fRegO/src/kernel.jl:52\n", "WARNING: DSP.TFFilter is deprecated, use PolynomialRatio instead.\n", " likely near /home/qebuild/.julia/packages/IJulia/fRegO/src/kernel.jl:52\n", "WARNING: DSP.TFFilter is deprecated, use PolynomialRatio instead.\n", " likely near /home/qebuild/.julia/packages/IJulia/fRegO/src/kernel.jl:52\n", "WARNING: DSP.TFFilter is deprecated, use PolynomialRatio instead.\n", " likely near /home/qebuild/.julia/packages/IJulia/fRegO/src/kernel.jl:52\n", "WARNING: DSP.TFFilter is deprecated, use PolynomialRatio instead.\n", " likely near /home/qebuild/.julia/packages/IJulia/fRegO/src/kernel.jl:52\n", "WARNING: DSP.TFFilter is deprecated, use PolynomialRatio instead.\n", " likely near /home/qebuild/.julia/packages/IJulia/fRegO/src/kernel.jl:52\n", "WARNING: DSP.TFFilter is deprecated, use PolynomialRatio instead.\n", " likely near /home/qebuild/.julia/packages/IJulia/fRegO/src/kernel.jl:52\n", "WARNING: DSP.TFFilter is deprecated, use PolynomialRatio instead.\n", " likely near /home/qebuild/.julia/packages/IJulia/fRegO/src/kernel.jl:52\n", "in #spectral_density#10 at /home/qebuild/.julia/packages/QuantEcon/Iww9D/src/arma.jl\n" ] }, { "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": { "filename": "arma.rst", "kernelspec": { "display_name": "Julia 1.2", "language": "julia", "name": "julia-1.2" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.2.0" }, "title": "Covariance Stationary Processes" }, "nbformat": 4, "nbformat_minor": 2 }