{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# A First Look at the Kalman Filter\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [A First Look at the Kalman Filter](#A-First-Look-at-the-Kalman-Filter) \n", " - [Overview](#Overview) \n", " - [The Basic Idea](#The-Basic-Idea) \n", " - [Convergence](#Convergence) \n", " - [Implementation](#Implementation) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "This lecture provides a simple and intuitive introduction to the Kalman filter, for those who either\n", "\n", "- have heard of the Kalman filter but don’t know how it works, or \n", "- know the Kalman filter equations, but don’t know where they come from \n", "\n", "\n", "For additional (more advanced) reading on the Kalman filter, see\n", "\n", "- [[LS18]](../zreferences.html#ljungqvist2012), section 2.7. \n", "- [[AM05]](../zreferences.html#andersonmoore2005) \n", "\n", "\n", "The second reference presents a comprehensive treatment of the Kalman filter.\n", "\n", "Required knowledge: Familiarity with matrix manipulations, multivariate normal distributions, covariance matrices, etc." ] }, { "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": [ "## The Basic Idea\n", "\n", "The Kalman filter has many applications in economics, but for now\n", "let’s pretend that we are rocket scientists.\n", "\n", "A missile has been launched from country Y and our mission is to track it.\n", "\n", "Let $ x \\in \\mathbb{R}^2 $ denote the current location of the missile—a\n", "pair indicating latitude-longitude coordinates on a map.\n", "\n", "At the present moment in time, the precise location $ x $ is unknown, but\n", "we do have some beliefs about $ x $.\n", "\n", "One way to summarize our knowledge is a point prediction $ \\hat x $\n", "\n", "- But what if the President wants to know the probability that the missile is currently over the Sea of Japan? \n", "- Then it is better to summarize our initial beliefs with a bivariate probability density $ p $. \n", " \n", " - $ \\int_E p(x)dx $ indicates the probability that we attach to the missile being in region $ E $ \n", " \n", "\n", "\n", "The density $ p $ is called our *prior* for the random variable $ x $.\n", "\n", "To keep things tractable in our example, we assume that our prior is Gaussian.\n", "In particular, we take\n", "\n", "\n", "\n", "$$\n", "p = N(\\hat x, \\Sigma) \\tag{1}\n", "$$\n", "\n", "where $ \\hat x $ is the mean of the distribution and $ \\Sigma $ is a\n", "$ 2 \\times 2 $ covariance matrix. In our simulations, we will suppose that\n", "\n", "\n", "\n", "$$\n", "\\hat x\n", "= \\left(\n", "\\begin{array}{c}\n", " 0.2 \\\\\n", " -0.2\n", "\\end{array}\n", " \\right),\n", "\\qquad\n", "\\Sigma\n", "= \\left(\n", "\\begin{array}{cc}\n", " 0.4 & 0.3 \\\\\n", " 0.3 & 0.45\n", "\\end{array}\n", " \\right) \\tag{2}\n", "$$\n", "\n", "This density $ p(x) $ is shown below as a contour map, with the center of the red ellipse being equal to $ \\hat x $" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using Plots, Distributions\n", "gr(fmt = :png); # plots setup" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false, "html-class": "collapse" }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# set up prior objects\n", "Σ = [0.4 0.3\n", " 0.3 0.45]\n", "x̂ = [0.2, -0.2]\n", "\n", "# define G and R from the equation y = Gx + N(0, R)\n", "G = I # this is a generic identity object that conforms to the right dimensions\n", "R = 0.5 .* Σ\n", "\n", "# define A and Q\n", "A = [1.2 0\n", " 0 -0.2]\n", "Q = 0.3Σ\n", "\n", "y = [2.3, -1.9]\n", "\n", "# plotting objects\n", "x_grid = range(-1.5, 2.9, length = 100)\n", "y_grid = range(-3.1, 1.7, length = 100)\n", "\n", "# generate distribution\n", "dist = MvNormal(x̂, Σ)\n", "two_args_to_pdf(dist) = (x, y) -> pdf(dist, [x, y]) # returns a function to be plotted\n", "\n", "# plot\n", "contour(x_grid, y_grid, two_args_to_pdf(dist), fill = false,\n", " color = :lighttest, cbar = false)\n", "contour!(x_grid, y_grid, two_args_to_pdf(dist), fill = false, lw=1,\n", " color = :grays, cbar = false)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Filtering Step\n", "\n", "We are now presented with some good news and some bad news.\n", "\n", "The good news is that the missile has been located by our sensors, which report that the current location is $ y = (2.3, -1.9) $.\n", "\n", "The next figure shows the original prior $ p(x) $ and the new reported\n", "location $ y $" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# plot the figure\n", "annotate!(y[1], y[2], \"y\", color = :black)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The bad news is that our sensors are imprecise.\n", "\n", "In particular, we should interpret the output of our sensor not as\n", "$ y=x $, but rather as\n", "\n", "\n", "\n", "$$\n", "y = G x + v, \\quad \\text{where} \\quad v \\sim N(0, R) \\tag{3}\n", "$$\n", "\n", "Here $ G $ and $ R $ are $ 2 \\times 2 $ matrices with $ R $\n", "positive definite. Both are assumed known, and the noise term $ v $ is assumed\n", "to be independent of $ x $.\n", "\n", "How then should we combine our prior $ p(x) = N(\\hat x, \\Sigma) $ and this\n", "new information $ y $ to improve our understanding of the location of the\n", "missile?\n", "\n", "As you may have guessed, the answer is to use Bayes’ theorem, which tells\n", "us to update our prior $ p(x) $ to $ p(x \\,|\\, y) $ via\n", "\n", "$$\n", "p(x \\,|\\, y) = \\frac{p(y \\,|\\, x) \\, p(x)} {p(y)}\n", "$$\n", "\n", "where $ p(y) = \\int p(y \\,|\\, x) \\, p(x) dx $.\n", "\n", "In solving for $ p(x \\,|\\, y) $, we observe that\n", "\n", "- $ p(x) = N(\\hat x, \\Sigma) $ \n", "- In view of [(3)](#equation-kl-measurement-model), the conditional density $ p(y \\,|\\, x) $ is $ N(Gx, R) $ \n", "- $ p(y) $ does not depend on $ x $, and enters into the calculations only as a normalizing constant \n", "\n", "\n", "Because we are in a linear and Gaussian framework, the updated density can be computed by calculating population linear regressions.\n", "\n", "In particular, the solution is known [1] to be\n", "\n", "$$\n", "p(x \\,|\\, y) = N(\\hat x^F, \\Sigma^F)\n", "$$\n", "\n", "where\n", "\n", "\n", "\n", "$$\n", "\\hat x^F := \\hat x + \\Sigma G' (G \\Sigma G' + R)^{-1}(y - G \\hat x)\n", "\\quad \\text{and} \\quad\n", "\\Sigma^F := \\Sigma - \\Sigma G' (G \\Sigma G' + R)^{-1} G \\Sigma \\tag{4}\n", "$$\n", "\n", "Here $ \\Sigma G' (G \\Sigma G' + R)^{-1} $ is the matrix of population regression coefficients of the hidden object $ x - \\hat x $ on the surprise $ y - G \\hat x $.\n", "\n", "This new density $ p(x \\,|\\, y) = N(\\hat x^F, \\Sigma^F) $ is shown in the next figure via contour lines and the color map.\n", "\n", "The original density is left in as contour lines for comparison" ] }, { "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": [ "# define posterior objects\n", "M = Σ * G' * inv(G * Σ * G' + R)\n", "x̂_F = x̂ + M * (y - G * x̂)\n", "Σ_F = Σ - M * G * Σ\n", "\n", "# plot the new density on the old plot\n", "newdist = MvNormal(x̂_F, Symmetric(Σ_F)) # because Σ_F\n", "contour!(x_grid, y_grid, two_args_to_pdf(newdist), fill = false,\n", " color = :lighttest, cbar = false)\n", "contour!(x_grid, y_grid, two_args_to_pdf(newdist), fill = false, levels = 7,\n", " color = :grays, cbar = false)\n", "contour!(x_grid, y_grid, two_args_to_pdf(dist), fill = false, levels = 7, lw=1,\n", " color = :grays, cbar = false)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our new density twists the prior $ p(x) $ in a direction determined by the new\n", "information $ y - G \\hat x $.\n", "\n", "In generating the figure, we set $ G $ to the identity matrix and $ R = 0.5 \\Sigma $ for $ \\Sigma $ defined in [(2)](#equation-kalman-dhxs).\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Forecast Step\n", "\n", "What have we achieved so far?\n", "\n", "We have obtained probabilities for the current location of the state (missile) given prior and current information.\n", "\n", "This is called “filtering” rather than forecasting, because we are filtering\n", "out noise rather than looking into the future\n", "\n", "- $ p(x \\,|\\, y) = N(\\hat x^F, \\Sigma^F) $ is called the *filtering distribution* \n", "\n", "\n", "But now let’s suppose that we are given another task: to predict the location of the missile after one unit of time (whatever that may be) has elapsed.\n", "\n", "To do this we need a model of how the state evolves.\n", "\n", "Let’s suppose that we have one, and that it’s linear and Gaussian. In particular,\n", "\n", "\n", "\n", "$$\n", "x_{t+1} = A x_t + w_{t+1}, \\quad \\text{where} \\quad w_t \\sim N(0, Q) \\tag{5}\n", "$$\n", "\n", "Our aim is to combine this law of motion and our current distribution $ p(x \\,|\\, y) = N(\\hat x^F, \\Sigma^F) $ to come up with a new *predictive* distribution for the location in one unit of time.\n", "\n", "In view of [(5)](#equation-kl-xdynam), all we have to do is introduce a random vector $ x^F \\sim N(\\hat x^F, \\Sigma^F) $ and work out the distribution of $ A x^F + w $ where $ w $ is independent of $ x^F $ and has distribution $ N(0, Q) $.\n", "\n", "Since linear combinations of Gaussians are Gaussian, $ A x^F + w $ is Gaussian.\n", "\n", "Elementary calculations and the expressions in [(4)](#equation-kl-filter-exp) tell us that\n", "\n", "$$\n", "\\mathbb{E} [A x^F + w]\n", "= A \\mathbb{E} x^F + \\mathbb{E} w\n", "= A \\hat x^F\n", "= A \\hat x + A \\Sigma G' (G \\Sigma G' + R)^{-1}(y - G \\hat x)\n", "$$\n", "\n", "and\n", "\n", "$$\n", "\\operatorname{Var} [A x^F + w]\n", "= A \\operatorname{Var}[x^F] A' + Q\n", "= A \\Sigma^F A' + Q\n", "= A \\Sigma A' - A \\Sigma G' (G \\Sigma G' + R)^{-1} G \\Sigma A' + Q\n", "$$\n", "\n", "The matrix $ A \\Sigma G' (G \\Sigma G' + R)^{-1} $ is often written as\n", "$ K_{\\Sigma} $ and called the *Kalman gain*.\n", "\n", "- The subscript $ \\Sigma $ has been added to remind us that $ K_{\\Sigma} $ depends on $ \\Sigma $, but not $ y $ or $ \\hat x $. \n", "\n", "\n", "Using this notation, we can summarize our results as follows.\n", "\n", "Our updated prediction is the density $ N(\\hat x_{new}, \\Sigma_{new}) $ where\n", "\n", "\n", "\n", "$$\n", "\\begin{aligned}\n", " \\hat x_{new} &:= A \\hat x + K_{\\Sigma} (y - G \\hat x) \\\\\n", " \\Sigma_{new} &:= A \\Sigma A' - K_{\\Sigma} G \\Sigma A' + Q \\nonumber\n", "\\end{aligned} \\tag{6}\n", "$$\n", "\n", "- The density $ p_{new}(x) = N(\\hat x_{new}, \\Sigma_{new}) $ is called the *predictive distribution*. \n", "\n", "\n", "The predictive distribution is the new density shown in the following figure, where\n", "the update has used parameters\n", "\n", "$$\n", "A\n", "= \\left(\n", "\\begin{array}{cc}\n", " 1.2 & 0.0 \\\\\n", " 0.0 & -0.2\n", "\\end{array}\n", " \\right),\n", " \\qquad\n", "Q = 0.3 * \\Sigma\n", "$$" ] }, { "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": [ "# get the predictive distribution\n", "new_x̂ = A * x̂_F\n", "new_Σ = A * Σ_F * A' + Q\n", "predictdist = MvNormal(new_x̂, Symmetric(new_Σ))\n", "\n", "# plot Density 3\n", "contour(x_grid, y_grid, two_args_to_pdf(predictdist), fill = false, lw = 1,\n", " color = :lighttest, cbar = false)\n", "contour!(x_grid, y_grid, two_args_to_pdf(dist),\n", " color = :grays, cbar = false)\n", "contour!(x_grid, y_grid, two_args_to_pdf(newdist), fill = false, levels = 7,\n", " color = :grays, cbar = false)\n", "annotate!(y[1], y[2], \"y\", color = :black)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Recursive Procedure\n", "\n", "\n", "\n", "Let’s look back at what we’ve done.\n", "\n", "We started the current period with a prior $ p(x) $ for the location $ x $ of the missile.\n", "\n", "We then used the current measurement $ y $ to update to $ p(x \\,|\\, y) $.\n", "\n", "Finally, we used the law of motion [(5)](#equation-kl-xdynam) for $ \\{x_t\\} $ to update to $ p_{new}(x) $.\n", "\n", "If we now step into the next period, we are ready to go round again, taking $ p_{new}(x) $\n", "as the current prior.\n", "\n", "Swapping notation $ p_t(x) $ for $ p(x) $ and $ p_{t+1}(x) $ for $ p_{new}(x) $, the full recursive procedure is:\n", "\n", "1. Start the current period with prior $ p_t(x) = N(\\hat x_t, \\Sigma_t) $. \n", "1. Observe current measurement $ y_t $. \n", "1. Compute the filtering distribution $ p_t(x \\,|\\, y) = N(\\hat x_t^F, \\Sigma_t^F) $ from $ p_t(x) $ and $ y_t $, applying Bayes rule and the conditional distribution [(3)](#equation-kl-measurement-model). \n", "1. Compute the predictive distribution $ p_{t+1}(x) = N(\\hat x_{t+1}, \\Sigma_{t+1}) $ from the filtering distribution and [(5)](#equation-kl-xdynam). \n", "1. Increment $ t $ by one and go to step 1. \n", "\n", "\n", "Repeating [(6)](#equation-kl-mlom0), the dynamics for $ \\hat x_t $ and $ \\Sigma_t $ are as follows\n", "\n", "\n", "\n", "$$\n", "\\begin{aligned}\n", " \\hat x_{t+1} &= A \\hat x_t + K_{\\Sigma_t} (y_t - G \\hat x_t) \\\\\n", " \\Sigma_{t+1} &= A \\Sigma_t A' - K_{\\Sigma_t} G \\Sigma_t A' + Q \\nonumber\n", "\\end{aligned} \\tag{7}\n", "$$\n", "\n", "These are the standard dynamic equations for the Kalman filter (see, for example, [[LS18]](../zreferences.html#ljungqvist2012), page 58).\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convergence\n", "\n", "The matrix $ \\Sigma_t $ is a measure of the uncertainty of our prediction $ \\hat x_t $ of $ x_t $.\n", "\n", "Apart from special cases, this uncertainty will never be fully resolved, regardless of how much time elapses.\n", "\n", "One reason is that our prediction $ \\hat x_t $ is made based on information available at $ t-1 $, not $ t $.\n", "\n", "Even if we know the precise value of $ x_{t-1} $ (which we don’t), the transition equation [(5)](#equation-kl-xdynam) implies that $ x_t = A x_{t-1} + w_t $.\n", "\n", "Since the shock $ w_t $ is not observable at $ t-1 $, any time $ t-1 $ prediction of $ x_t $ will incur some error (unless $ w_t $ is degenerate).\n", "\n", "However, it is certainly possible that $ \\Sigma_t $ converges to a constant matrix as $ t \\to \\infty $.\n", "\n", "To study this topic, let’s expand the second equation in [(7)](#equation-kalman-lom):\n", "\n", "\n", "\n", "$$\n", "\\Sigma_{t+1} = A \\Sigma_t A' - A \\Sigma_t G' (G \\Sigma_t G' + R)^{-1} G \\Sigma_t A' + Q \\tag{8}\n", "$$\n", "\n", "This is a nonlinear difference equation in $ \\Sigma_t $.\n", "\n", "A fixed point of [(8)](#equation-kalman-sdy) is a constant matrix $ \\Sigma $ such that\n", "\n", "\n", "\n", "$$\n", "\\Sigma = A \\Sigma A' - A \\Sigma G' (G \\Sigma G' + R)^{-1} G \\Sigma A' + Q \\tag{9}\n", "$$\n", "\n", "Equation [(8)](#equation-kalman-sdy) is known as a discrete time Riccati difference equation.\n", "\n", "Equation [(9)](#equation-kalman-dare) is known as a [discrete time algebraic Riccati equation](https://en.wikipedia.org/wiki/Algebraic_Riccati_equation).\n", "\n", "Conditions under which a fixed point exists and the sequence $ \\{\\Sigma_t\\} $ converges to it are discussed in [[AHMS96]](../zreferences.html#ahms1996) and [[AM05]](../zreferences.html#andersonmoore2005), chapter 4.\n", "\n", "A sufficient (but not necessary) condition is that all the eigenvalues $ \\lambda_i $ of $ A $ satisfy $ |\\lambda_i| < 1 $ (cf. e.g., [[AM05]](../zreferences.html#andersonmoore2005), p. 77).\n", "\n", "(This strong condition assures that the unconditional distribution of $ x_t $ converges as $ t \\rightarrow + \\infty $)\n", "\n", "In this case, for any initial choice of $ \\Sigma_0 $ that is both nonnegative and symmetric, the sequence $ \\{\\Sigma_t\\} $ in [(8)](#equation-kalman-sdy) converges to a nonnegative symmetric matrix $ \\Sigma $ that solves [(9)](#equation-kalman-dare)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "\n", "\n", "The [QuantEcon.jl](http://quantecon.org/quantecon-jl) package is able to implement the Kalman filter by using methods for the type `Kalman`\n", "\n", "- Instance data consists of: \n", " \n", " - The parameters $ A, G, Q, R $ of a given model \n", " - the moments $ (\\hat x_t, \\Sigma_t) $ of the current prior \n", " \n", "- The type `Kalman` from the [QuantEcon.jl](http://quantecon.org/quantecon-jl) package has a number of methods, some that we will wait to use until we study more advanced applications in subsequent lectures. \n", "- Methods pertinent for this lecture are: \n", " \n", " - `prior_to_filtered`, which updates $ (\\hat x_t, \\Sigma_t) $ to $ (\\hat x_t^F, \\Sigma_t^F) $ \n", " - `filtered_to_forecast`, which updates the filtering distribution to the predictive distribution – which becomes the new prior $ (\\hat x_{t+1}, \\Sigma_{t+1}) $ \n", " - `update`, which combines the last two methods \n", " - a `stationary_values`, which computes the solution to [(9)](#equation-kalman-dare) and the corresponding (stationary) Kalman gain \n", " \n", "\n", "\n", "You can view the program [on GitHub](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/kalman.jl)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Consider the following simple application of the Kalman filter, loosely based\n", "on [[LS18]](../zreferences.html#ljungqvist2012), section 2.9.2.\n", "\n", "Suppose that\n", "\n", "- all variables are scalars \n", "- the hidden state $ \\{x_t\\} $ is in fact constant, equal to some $ \\theta \\in \\mathbb{R} $ unknown to the modeler \n", "\n", "\n", "State dynamics are therefore given by [(5)](#equation-kl-xdynam) with $ A=1 $, $ Q=0 $ and $ x_0 = \\theta $.\n", "\n", "The measurement equation is $ y_t = \\theta + v_t $ where $ v_t $ is $ N(0,1) $ and iid.\n", "\n", "The task of this exercise to simulate the model and, using the code from `kalman.jl`, plot the first five predictive densities $ p_t(x) = N(\\hat x_t, \\Sigma_t) $.\n", "\n", "As shown in [[LS18]](../zreferences.html#ljungqvist2012), sections 2.9.1–2.9.2, these distributions asymptotically put all mass on the unknown value $ \\theta $.\n", "\n", "In the simulation, take $ \\theta = 10 $, $ \\hat x_0 = 8 $ and $ \\Sigma_0 = 1 $.\n", "\n", "Your figure should – modulo randomness – look something like this\n", "\n", "\n", "\n", " \n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "The preceding figure gives some support to the idea that probability mass\n", "converges to $ \\theta $.\n", "\n", "To get a better idea, choose a small $ \\epsilon > 0 $ and calculate\n", "\n", "$$\n", "z_t := 1 - \\int_{\\theta - \\epsilon}^{\\theta + \\epsilon} p_t(x) dx\n", "$$\n", "\n", "for $ t = 0, 1, 2, \\ldots, T $.\n", "\n", "Plot $ z_t $ against $ T $, setting $ \\epsilon = 0.1 $ and $ T = 600 $.\n", "\n", "Your figure should show error erratically declining something like this\n", "\n", "\n", "\n", " \n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "As discussed [above](#kalman-convergence), if the shock sequence $ \\{w_t\\} $ is not degenerate, then it is not in general possible to predict $ x_t $ without error at time $ t-1 $ (and this would be the case even if we could observe $ x_{t-1} $).\n", "\n", "Let’s now compare the prediction $ \\hat x_t $ made by the Kalman filter\n", "against a competitor who **is** allowed to observe $ x_{t-1} $.\n", "\n", "This competitor will use the conditional expectation $ \\mathbb E[ x_t\n", "\\,|\\, x_{t-1}] $, which in this case is $ A x_{t-1} $.\n", "\n", "The conditional expectation is known to be the optimal prediction method in terms of minimizing mean squared error.\n", "\n", "(More precisely, the minimizer of $ \\mathbb E \\, \\| x_t - g(x_{t-1}) \\|^2 $ with respect to $ g $ is $ g^*(x_{t-1}) := \\mathbb E[ x_t \\,|\\, x_{t-1}] $)\n", "\n", "Thus we are comparing the Kalman filter against a competitor who has more\n", "information (in the sense of being able to observe the latent state) and\n", "behaves optimally in terms of minimizing squared error.\n", "\n", "Our horse race will be assessed in terms of squared error.\n", "\n", "In particular, your task is to generate a graph plotting observations of both $ \\| x_t - A x_{t-1} \\|^2 $ and $ \\| x_t - \\hat x_t \\|^2 $ against $ t $ for $ t = 1, \\ldots, 50 $.\n", "\n", "For the parameters, set $ G = I, R = 0.5 I $ and $ Q = 0.3 I $, where $ I $ is\n", "the $ 2 \\times 2 $ identity.\n", "\n", "Set\n", "\n", "$$\n", "A\n", "= \\left(\n", "\\begin{array}{cc}\n", " 0.5 & 0.4 \\\\\n", " 0.6 & 0.3\n", "\\end{array}\n", " \\right)\n", "$$\n", "\n", "To initialize the prior density, set\n", "\n", "$$\n", "\\Sigma_0\n", "= \\left(\n", "\\begin{array}{cc}\n", " 0.9 & 0.3 \\\\\n", " 0.3 & 0.9\n", "\\end{array}\n", " \\right)\n", "$$\n", "\n", "and $ \\hat x_0 = (8, 8) $.\n", "\n", "Finally, set $ x_0 = (0, 0) $.\n", "\n", "You should end up with a figure similar to the following (modulo randomness)\n", "\n", "\n", "\n", " \n", "Observe how, after an initial learning period, the Kalman filter performs quite well, even relative to the competitor who predicts optimally with knowledge of the latent state.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4\n", "\n", "Try varying the coefficient $ 0.3 $ in $ Q = 0.3 I $ up and down.\n", "\n", "Observe how the diagonal values in the stationary solution $ \\Sigma $ (see [(9)](#equation-kalman-dare)) increase and decrease in line with this coefficient.\n", "\n", "The interpretation is that more randomness in the law of motion for $ x_t $ causes more (permanent) uncertainty in prediction." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using QuantEcon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# parameters\n", "θ = 10\n", "A, G, Q, R = 1.0, 1.0, 0.0, 1.0\n", "x̂_0, Σ_0 = 8.0, 1.0\n", "\n", "# initialize Kalman filter\n", "kalman = Kalman(A, G, Q, R)\n", "set_state!(kalman, x̂_0, Σ_0)\n", "\n", "xgrid = range(θ - 5, θ + 2, length = 200)\n", "densities = zeros(200, 5) # one column per round of updating\n", "for i in 1:5\n", " # record the current predicted mean and variance, and plot their densities\n", " m, v = kalman.cur_x_hat, kalman.cur_sigma\n", " densities[:, i] = pdf.(Normal(m, sqrt(v)), xgrid)\n", "\n", " # generate the noisy signal\n", " y = θ + randn()\n", "\n", " # update the Kalman filter\n", " update!(kalman, y)\n", "end\n", "\n", "labels = [\"t=1\", \"t=2\", \"t=3\", \"t=4\", \"t=5\"]\n", "plot(xgrid, densities, label = labels, legend = :topleft, grid = false,\n", " title = \"First 5 densities when theta = $θ\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Random, Expectations\n", "Random.seed!(43) # reproducible results\n", "ϵ = 0.1\n", "kalman = Kalman(A, G, Q, R)\n", "set_state!(kalman, x̂_0, Σ_0)\n", "nodes, weights = qnwlege(21, θ-ϵ, θ+ϵ)\n", "\n", "T = 600\n", "z = zeros(T)\n", "for t in 1:T\n", " # record the current predicted mean and variance, and plot their densities\n", " m, v = kalman.cur_x_hat, kalman.cur_sigma\n", " dist = Truncated(Normal(m, sqrt(v)), θ-30*ϵ, θ+30*ϵ) # define on compact interval, so we can use gridded expectation\n", " E = expectation(dist, nodes) # nodes ∈ [θ-ϵ, θ+ϵ]\n", " integral = E(x -> 1) # just take the pdf integral\n", " z[t] = 1. - integral\n", " # generate the noisy signal and update the Kalman filter\n", " update!(kalman, θ + randn())\n", "end\n", "\n", "plot(1:T, z, fillrange = 0, color = :blue, fillalpha = 0.2, grid = false, xlims=(0, T),\n", " legend = false)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Eigenvalues of A:\n", "[-0.10000000000000003, 0.8999999999999999]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Stationary prediction error variance:\n", "[0.4032910794778669 0.10507180275061759; 0.1050718027506176 0.41061709375220456]\n" ] }, { "data": { "image/png": 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" }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# define A, Q, G, R\n", "G = I + zeros(2, 2)\n", "R = 0.5 .* G\n", "A = [0.5 0.4\n", " 0.6 0.3]\n", "Q = 0.3 .* G\n", "\n", "# define the prior density\n", "Σ = [0.9 0.3\n", " 0.3 0.9]\n", "x̂ = [8, 8]\n", "\n", "# initialize the Kalman filter\n", "kn = Kalman(A, G, Q, R)\n", "set_state!(kn, x̂, Σ)\n", "\n", "# set the true initial value of the state\n", "x = zeros(2)\n", "\n", "# print eigenvalues of A\n", "println(\"Eigenvalues of A:\\n$(eigvals(A))\")\n", "\n", "# print stationary Σ\n", "S, K = stationary_values(kn)\n", "println(\"Stationary prediction error variance:\\n$S\")\n", "\n", "# generate the plot\n", "T = 50\n", "e1 = zeros(T)\n", "e2 = similar(e1)\n", "for t in 1:T\n", "\n", " # generate signal and update prediction\n", " dist = MultivariateNormal(G * x, R)\n", " y = rand(dist)\n", " update!(kn, y)\n", "\n", " # update state and record error\n", " Ax = A * x\n", " x = rand(MultivariateNormal(Ax, Q))\n", " e1[t] = sum((a - b)^2 for (a, b) in zip(x, kn.cur_x_hat))\n", " e2[t] = sum((a - b)^2 for (a, b) in zip(x, Ax))\n", "end\n", "\n", "plot(1:T, e1, color = :black, linewidth = 2, alpha = 0.6, label = \"Kalman filter error\",\n", " grid = false)\n", "plot!(1:T, e2, color = :green, linewidth = 2, alpha = 0.6,\n", " label = \"conditional expectation error\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Footnotes**\n", "\n", "

[1] See, for example, page 93 of [[Bis06]](../zreferences.html#bishop2006). To get from his expressions to the ones used above, you will also need to apply the [Woodbury matrix identity](https://en.wikipedia.org/wiki/Woodbury_matrix_identity)." ] } ], "metadata": { "date": 1591310628.2812724, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "kalman.rst", "filename_with_path": "tools_and_techniques/kalman", "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": "A First Look at the Kalman Filter" }, "nbformat": 4, "nbformat_minor": 2 }