{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Estimation of Spectra\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Estimation of Spectra](#Estimation-of-Spectra) \n", " - [Overview](#Overview) \n", " - [Periodograms](#Periodograms) \n", " - [Smoothing](#Smoothing) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "In a [previous lecture](arma.html#arma) we covered some fundamental properties of covariance stationary linear stochastic processes.\n", "\n", "One objective for that lecture was to introduce spectral densities — a standard and very useful technique for analyzing such processes.\n", "\n", "In this lecture we turn to the problem of estimating spectral densities and other related quantities from data.\n", "\n", "\n", "\n", "Estimates of the spectral density are computed using what is known as a periodogram — which in\n", "turn is computed via the famous [fast Fourier transform](https://en.wikipedia.org/wiki/Fast_Fourier_transform).\n", "\n", "Once the basic technique has been explained, we will apply it to the analysis of several key macroeconomic time series.\n", "\n", "For supplementary reading, see [[Sar87]](../zreferences.html#sargent1987) or [[CC08]](../zreferences.html#cryerchan2008)." ] }, { "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": [ "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Periodograms\n", "\n", "[Recall that](arma.html#arma-specd) the spectral density $ f $ of a covariance stationary process with\n", "autocorrelation function $ \\gamma $ can be written\n", "\n", "$$\n", "f(\\omega) = \\gamma(0) + 2 \\sum_{k \\geq 1} \\gamma(k) \\cos(\\omega k),\n", "\\qquad \\omega \\in \\mathbb R\n", "$$\n", "\n", "Now consider the problem of estimating the spectral density of a given time series, when $ \\gamma $ is unknown.\n", "\n", "In particular, let $ X_0, \\ldots, X_{n-1} $ be $ n $ consecutive observations of a single time series that is assumed to be covariance stationary.\n", "\n", "The most common estimator of the spectral density of this process is the *periodogram* of $ X_0, \\ldots, X_{n-1} $, which is defined as\n", "\n", "\n", "\n", "$$\n", "I(\\omega)\n", ":= \\frac{1}{n} \\left| \\sum_{t=0}^{n-1} X_t e^{i t \\omega} \\right|^2,\n", "\\qquad \\omega \\in \\mathbb R \\tag{1}\n", "$$\n", "\n", "(Recall that $ |z| $ denotes the modulus of complex number $ z $)\n", "\n", "Alternatively, $ I(\\omega) $ can be expressed as\n", "\n", "$$\n", "I(\\omega)\n", "= \\frac{1}{n}\n", "\\left\\{\n", "\\left[\\sum_{t=0}^{n-1} X_t \\cos(\\omega t) \\right]^2\n", "+\n", "\\left[\\sum_{t=0}^{n-1} X_t \\sin(\\omega t) \\right]^2\n", "\\right\\}\n", "$$\n", "\n", "It is straightforward to show that the function $ I $ is even and $ 2\n", "\\pi $-periodic (i.e., $ I(\\omega) = I(-\\omega) $ and $ I(\\omega +\n", "2\\pi) = I(\\omega) $ for all $ \\omega \\in \\mathbb R $).\n", "\n", "From these two results, you will be able to verify that the values of\n", "$ I $ on $ [0, \\pi] $ determine the values of $ I $ on all of\n", "$ \\mathbb R $.\n", "\n", "The next section helps to explain the connection between the periodogram and the spectral density." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interpretation\n", "\n", "\n", "\n", "To interpret the periodogram, it is convenient to focus on its values at the *Fourier frequencies*\n", "\n", "$$\n", "\\omega_j := \\frac{2 \\pi j}{n},\n", "\\quad j = 0, \\ldots, n - 1\n", "$$\n", "\n", "In what sense is $ I(\\omega_j) $ an estimate of $ f(\\omega_j) $?\n", "\n", "The answer is straightforward, although it does involve some algebra.\n", "\n", "With a bit of effort one can show that, for any integer $ j > 0 $,\n", "\n", "$$\n", "\\sum_{t=0}^{n-1} e^{i t \\omega_j }\n", "= \\sum_{t=0}^{n-1} \\exp \\left\\{ i 2 \\pi j \\frac{t}{n} \\right\\} = 0\n", "$$\n", "\n", "Letting $ \\bar X $ denote the sample mean $ n^{-1} \\sum_{t=0}^{n-1} X_t $, we then have\n", "\n", "$$\n", "n I(\\omega_j)\n", " = \\left| \\sum_{t=0}^{n-1} (X_t - \\bar X) e^{i t \\omega_j } \\right|^2\n", " = \\sum_{t=0}^{n-1} (X_t - \\bar X) e^{i t \\omega_j }\n", "\\sum_{r=0}^{n-1} (X_r - \\bar X) e^{-i r \\omega_j }\n", "$$\n", "\n", "By carefully working through the sums, one can transform this to\n", "\n", "$$\n", "n I(\\omega_j)\n", "= \\sum_{t=0}^{n-1} (X_t - \\bar X)^2\n", "+ 2 \\sum_{k=1}^{n-1} \\sum_{t=k}^{n-1} (X_t - \\bar X)(X_{t-k} - \\bar X)\n", "\\cos(\\omega_j k)\n", "$$\n", "\n", "Now let\n", "\n", "$$\n", "\\hat \\gamma(k)\n", ":= \\frac{1}{n} \\sum_{t=k}^{n-1} (X_t - \\bar X)(X_{t-k} - \\bar X),\n", "\\qquad k = 0,1,\\ldots, n-1\n", "$$\n", "\n", "This is the sample autocovariance function, the natural “plug-in estimator” of the [autocovariance function](arma.html#arma-defs) $ \\gamma $.\n", "\n", "(“Plug-in estimator” is an informal term for an estimator found by replacing expectations with sample means)\n", "\n", "With this notation, we can now write\n", "\n", "$$\n", "I(\\omega_j)\n", "= \\hat \\gamma(0)\n", "+ 2 \\sum_{k=1}^{n-1} \\hat \\gamma(k) \\cos(\\omega_j k)\n", "$$\n", "\n", "Recalling our expression for $ f $ given [above](#periodograms),\n", "we see that $ I(\\omega_j) $ is just a sample analog of $ f(\\omega_j) $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculation\n", "\n", "\n", "\n", "Let’s now consider how to compute the periodogram as defined in [(1)](#equation-estspec-p).\n", "\n", "There are already functions available that will do this for us\n", "— an example is `periodogram` in the `DSP.jl` package.\n", "\n", "However, it is very simple to replicate their results, and this will give us a platform to make useful extensions.\n", "\n", "The most common way to calculate the periodogram is via the discrete Fourier transform,\n", "which in turn is implemented through the [fast Fourier transform](https://en.wikipedia.org/wiki/Fast_Fourier_transform) algorithm.\n", "\n", "In general, given a sequence $ a_0, \\ldots, a_{n-1} $, the discrete\n", "Fourier transform computes the sequence\n", "\n", "$$\n", "A_j := \\sum_{t=0}^{n-1} a_t \\exp \\left\\{ i 2 \\pi \\frac{tj}{n} \\right\\},\n", "\\qquad j = 0, \\ldots, n-1\n", "$$\n", "\n", "With $ a_0, \\ldots, a_{n-1} $ stored in Julia array `a`, the function call `fft(a)` returns the values $ A_0, \\ldots, A_{n-1} $ as a Julia array.\n", "\n", "It follows that, when the data $ X_0, \\ldots, X_{n-1} $ are stored in array `X`, the values $ I(\\omega_j) $ at the Fourier frequencies, which are given by\n", "\n", "$$\n", "\\frac{1}{n} \\left| \\sum_{t=0}^{n-1} X_t \\exp \\left\\{ i 2 \\pi \\frac{t j}{n} \\right\\} \\right|^2,\n", "\\qquad j = 0, \\ldots, n-1\n", "$$\n", "\n", "can be computed by `abs(fft(X)).^2 / length(X)`.\n", "\n", "Note: The Julia function `abs` acts elementwise, and correctly handles complex numbers (by computing their modulus, which is exactly what we need).\n", "\n", "A function called `periodogram` that puts all this together can be found [here](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/estspec.jl).\n", "\n", "Let’s generate some data for this function using the `ARMA` type from [QuantEcon.jl](https://github.com/QuantEcon/QuantEcon.jl) (see the [lecture on linear processes](arma.html#arma) for more details).\n", "\n", "Here’s a code snippet that, once the preceding code has been run, generates data from the process\n", "\n", "\n", "\n", "$$\n", "X_t = 0.5 X_{t-1} + \\epsilon_t - 0.8 \\epsilon_{t-2} \\tag{2}\n", "$$\n", "\n", "where $ \\{ \\epsilon_t \\} $ is white noise with unit variance, and compares the periodogram to the actual spectral density" ] }, { "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 QuantEcon, Plots, Random\n", "gr(fmt = :png);\n", "Random.seed!(42) # For reproducible results.\n", "\n", "n = 40 # Data size\n", "ϕ = 0.5 # AR parameter\n", "θ = [0, -0.8] # MA parameter\n", "σ = 1.0\n", "lp = ARMA(ϕ, θ, σ)\n", "X = simulation(lp, ts_length = n)\n", "\n", "x, y = periodogram(X)\n", "x_sd, y_sd = spectral_density(lp, two_pi=false, res=120)\n", "\n", "plot(x, y,linecolor=\"blue\", linewidth=2, linealpha=0.5, lab=\"periodogram\")\n", "plot!(x_sd, y_sd, linecolor=\"red\", linewidth=2, linealpha=0.8, lab=\"spectral density\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This estimate looks rather disappointing, but the data size is only 40, so\n", "perhaps it’s not surprising that the estimate is poor.\n", "\n", "However, if we try again with `n = 1200` the outcome is not much better\n", "\n", "\n", "\n", " \n", "The periodogram is far too irregular relative to the underlying spectral density.\n", "\n", "This brings us to our next topic." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing\n", "\n", "\n", "\n", "There are two related issues here.\n", "\n", "One is that, given the way the fast Fourier transform is implemented, the\n", "number of points $ \\omega $ at which $ I(\\omega) $ is estimated\n", "increases in line with the amount of data.\n", "\n", "In other words, although we have more data, we are also using it to estimate more values.\n", "\n", "A second issue is that densities of all types are fundamentally hard to\n", "estimate without parametric assumptions.\n", "\n", "\n", "\n", "Typically, nonparametric estimation of densities requires some degree of smoothing.\n", "\n", "The standard way that smoothing is applied to periodograms is by taking local averages.\n", "\n", "In other words, the value $ I(\\omega_j) $ is replaced with a weighted\n", "average of the adjacent values\n", "\n", "$$\n", "I(\\omega_{j-p}), I(\\omega_{j-p+1}), \\ldots, I(\\omega_j), \\ldots, I(\\omega_{j+p})\n", "$$\n", "\n", "This weighted average can be written as\n", "\n", "\n", "\n", "$$\n", "I_S(\\omega_j) := \\sum_{\\ell = -p}^{p} w(\\ell) I(\\omega_{j+\\ell}) \\tag{3}\n", "$$\n", "\n", "where the weights $ w(-p), \\ldots, w(p) $ are a sequence of $ 2p + 1 $ nonnegative\n", "values summing to one.\n", "\n", "In generally, larger values of $ p $ indicate more smoothing — more on\n", "this below.\n", "\n", "The next figure shows the kind of sequence typically used.\n", "\n", "Note the smaller weights towards the edges and larger weights in the center, so that more distant values from $ I(\\omega_j) $ have less weight than closer ones in the sum [(3)](#equation-estspec-ws)" ] }, { "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": [ "function hanning_window(M)\n", " w = [0.5 - 0.5 * cos(2 * pi * n / (M - 1)) for n = 0:(M-1)]\n", " return w\n", "end\n", "\n", "window = hanning_window(25) / sum(hanning_window(25))\n", "x = range(-12, 12, length = 25)\n", "plot(x, window, color=\"darkblue\", title=\"Hanning window\", ylabel=\"Weights\",\n", " xlabel=\"Position in sequence of weights\", legend=false, grid=false)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Estimation with Smoothing\n", "\n", "\n", "\n", "Our next step is to provide code that will not only estimate the periodogram but also provide smoothing as required.\n", "\n", "Such functions have been written in [estspec.jl](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/estspec.jl) and are available once you’ve installed [QuantEcon.jl](http://quantecon.org/quantecon-jl).\n", "\n", "The [GitHub listing](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/estspec.jl) displays three functions, `smooth()`, `periodogram()`, `ar_periodogram()`. We will discuss the first two here and the third one [below](#ar-periodograms).\n", "\n", "The `periodogram()` function returns a periodogram, optionally smoothed via the `smooth()` function.\n", "\n", "Regarding the `smooth()` function, since smoothing adds a nontrivial amount of computation, we have applied a fairly terse array-centric method based around `conv`.\n", "\n", "Readers are left either to explore or simply to use this code according to their interests.\n", "\n", "The next three figures each show smoothed and unsmoothed periodograms, as well as the population or “true” spectral density.\n", "\n", "(The model is the same as before — see equation [(2)](#equation-esp-arma) — and there are 400 observations)\n", "\n", "From top figure to bottom, the window length is varied from small to large.\n", "\n", "\n", "\n", "\n", "\n", " \n", "In looking at the figure, we can see that for this model and data size, the\n", "window length chosen in the middle figure provides the best fit.\n", "\n", "Relative to this value, the first window length provides insufficient\n", "smoothing, while the third gives too much smoothing.\n", "\n", "Of course in real estimation problems the true spectral density is not visible\n", "and the choice of appropriate smoothing will have to be made based on\n", "judgement/priors or some other theory.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pre-Filtering and Smoothing\n", "\n", "\n", "\n", "In the [code listing](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/estspec.jl) we showed three functions from the file `estspec.jl`.\n", "\n", "The third function in the file (`ar_periodogram()`) adds a pre-processing step to periodogram smoothing.\n", "\n", "First we describe the basic idea, and after that we give the code.\n", "\n", "The essential idea is to\n", "\n", "1. Transform the data in order to make estimation of the spectral density more efficient. \n", "1. Compute the periodogram associated with the transformed data. \n", "1. Reverse the effect of the transformation on the periodogram, so that it now\n", " estimates the spectral density of the original process. \n", "\n", "\n", "Step 1 is called *pre-filtering* or *pre-whitening*, while step 3 is called *recoloring*.\n", "\n", "The first step is called pre-whitening because the\n", "transformation is usually designed to turn the data into something closer to white noise.\n", "\n", "Why would this be desirable in terms of spectral density estimation?\n", "\n", "The reason is that we are smoothing our estimated periodogram based on\n", "estimated values at nearby points — recall [(3)](#equation-estspec-ws).\n", "\n", "The underlying assumption that makes this a good idea is that the true\n", "spectral density is relatively regular — the value of $ I(\\omega) $ is close\n", "to that of $ I(\\omega') $ when $ \\omega $ is close to $ \\omega' $.\n", "\n", "This will not be true in all cases, but it is certainly true for white noise.\n", "\n", "For white noise, $ I $ is as regular as possible — [it is a constant function](arma.html#arma-wnsd).\n", "\n", "In this case, values of $ I(\\omega') $ at points $ \\omega' $ near to $ \\omega $\n", "provided the maximum possible amount of information about the value $ I(\\omega) $.\n", "\n", "Another way to put this is that if $ I $ is relatively constant, then we can use a large amount of smoothing without introducing too much bias.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The AR(1) Setting\n", "\n", "\n", "\n", "Let’s examine this idea more carefully in a particular setting — where\n", "the data are assumed to be generated by an AR(1) process.\n", "\n", "(More general ARMA settings can be handled using similar techniques to those described below)\n", "\n", "Suppose in particular that $ \\{X_t\\} $ is covariance stationary and AR(1),\n", "with\n", "\n", "\n", "\n", "$$\n", "X_{t+1} = \\mu + \\phi X_t + \\epsilon_{t+1} \\tag{4}\n", "$$\n", "\n", "where $ \\mu $ and $ \\phi \\in (-1, 1) $ are unknown parameters and $ \\{ \\epsilon_t \\} $ is white noise.\n", "\n", "It follows that if we regress $ X_{t+1} $ on $ X_t $ and an intercept, the residuals\n", "will approximate white noise.\n", "\n", "Let\n", "\n", "- $ g $ be the spectral density of $ \\{ \\epsilon_t \\} $ — a constant function, as discussed above \n", "- $ I_0 $ be the periodogram estimated from the residuals — an estimate of $ g $ \n", "- $ f $ be the spectral density of $ \\{ X_t \\} $ — the object we are trying to estimate \n", "\n", "\n", "In view of [an earlier result](arma.html#arma-spec-den) we obtained while discussing ARMA processes, $ f $ and $ g $ are related by\n", "\n", "\n", "\n", "$$\n", "f(\\omega) = \\left| \\frac{1}{1 - \\phi e^{i\\omega}} \\right|^2 g(\\omega) \\tag{5}\n", "$$\n", "\n", "This suggests that the recoloring step, which constructs an estimate $ I $ of $ f $ from $ I_0 $, should set\n", "\n", "$$\n", "I(\\omega) = \\left| \\frac{1}{1 - \\hat \\phi e^{i\\omega}} \\right|^2 I_0(\\omega)\n", "$$\n", "\n", "where $ \\hat \\phi $ is the OLS estimate of $ \\phi $.\n", "\n", "The code for `ar_periodogram()` — the third function in `estspec.jl` — does exactly this. (See the code [here](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/estspec.jl)).\n", "\n", "The next figure shows realizations of the two kinds of smoothed periodograms\n", "\n", "1. “standard smoothed periodogram”, the ordinary smoothed periodogram, and \n", "1. “AR smoothed periodogram”, the pre-whitened and recolored one generated by `ar_periodogram()` \n", "\n", "\n", "The periodograms are calculated from time series drawn from [(4)](#equation-estspec-ar-dgp) with $ \\mu = 0 $ and $ \\phi = -0.9 $.\n", "\n", "Each time series is of length 150.\n", "\n", "The difference between the three subfigures is just randomness — each one uses a different draw of the time series.\n", "\n", "\n", "\n", "\n", "\n", " \n", "In all cases, periodograms are fit with the “hamming” window and window length of 65.\n", "\n", "Overall, the fit of the AR smoothed periodogram is much better, in the sense\n", "of being closer to the true spectral density." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Replicate [this figure](#fig-window-smoothing) (modulo randomness).\n", "\n", "The model is as in equation [(2)](#equation-esp-arma) and there are 400 observations.\n", "\n", "For the smoothed periodogram, the window type is “hamming”.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Replicate [this figure](#fig-ar-smoothed-periodogram) (modulo randomness).\n", "\n", "The model is as in equation [(4)](#equation-estspec-ar-dgp), with $ \\mu = 0 $, $ \\phi = -0.9 $\n", "and 150 observations in each time series.\n", "\n", "All periodograms are fit with the “hamming” window and window length of 65." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [], "source": [ "n = 400\n", "ϕ = 0.5\n", "θ = [0, -0.8]\n", "σ = 1.0\n", "lp = ARMA(ϕ, θ, 1.0)\n", "X = simulation(lp, ts_length = n)\n", "\n", "xs = []\n", "x_sds = []\n", "x_sms = []\n", "ys = []\n", "y_sds = []\n", "y_sms = []\n", "titles = []\n", "\n", "for (i, wl) in enumerate([15, 55, 175]) # window lengths\n", " x, y = periodogram(X)\n", " push!(xs, x)\n", " push!(ys, y)\n", "\n", " x_sd, y_sd = spectral_density(lp, two_pi=false, res=120)\n", " push!(x_sds, x_sd)\n", " push!(y_sds, y_sd)\n", "\n", " x, y_smoothed = periodogram(X, \"hamming\", wl)\n", " push!(x_sms, x)\n", " push!(y_sms, y_smoothed)\n", "\n", " t = \"window length = $wl\"\n", " push!(titles, t)\n", "end" ] }, { "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": [ "plot(xs, ys, layout=(3,1), color=:blue, alpha=0.5,\n", " linewidth=2, label=[\"periodogram\" \"\" \"\"])\n", "plot!(x_sds, y_sds, layout=(3,1), color=:red, alpha=0.8,\n", " linewidth=2, label=[\"spectral density\" \"\" \"\"])\n", "plot!(x_sms, y_sms, layout=(3,1), color=:black,\n", " linewidth=2, label=[\"smoothed periodogram\" \"\" \"\"])\n", "plot!(title=reshape(titles,1,length(titles)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lp2 = ARMA(-0.9, 0.0, 1.0)\n", "wl = 65\n", "p = plot(layout=(3,1))\n", "\n", "for i in 1:3\n", " X = simulation(lp2,ts_length=150)\n", " plot!(p[i],xlims = (0,pi))\n", "\n", " x_sd, y_sd = spectral_density(lp2,two_pi=false, res=180)\n", " plot!(p[i],x_sd, y_sd, linecolor=:red, linestyle=:solid,\n", " yscale=:log10, linewidth=2, linealpha=0.75,\n", " label=\"spectral density\",legend=:topleft)\n", "\n", " x, y_smoothed = periodogram(X, \"hamming\", wl)\n", " plot!(p[i],x, y_smoothed, linecolor=:black, linestyle=:solid,\n", " yscale=:log10, linewidth=2, linealpha=0.75,\n", " label=\"standard smoothed periodogram\",legend=:topleft)\n", "\n", " x, y_ar = ar_periodogram(X, \"hamming\", wl)\n", " plot!(p[i],x, y_ar, linecolor=:blue, linestyle=:solid,\n", " yscale=:log10, linewidth=2, linealpha=0.75,\n", " label=\"AR smoothed periodogram\",legend=:topleft)\n", "end\n", "p" ] } ], "metadata": { "date": 1591310626.8002026, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "estspec.rst", "filename_with_path": "time_series_models/estspec", "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": "Estimation of Spectra" }, "nbformat": 4, "nbformat_minor": 2 }