www.gusucode.com > econ 案例源码程序 matlab代码 > econ/FilterStatesOfAStateSpaceModelExample.m

    %% Filter States of State-Space Model
% This example shows how to filter states of a known, time-invariant,
% state-space model.
%%
% Suppose that a latent process is an AR(1).  Subsequently, the state
% equation is 
%
% $$x_t = 0.5x_{t-1} + u_t,$$
%
% where $u_t$ is Gaussian with mean 0 and standard deviation 1.
%%
% Generate a random series of 100 observations from $x_t$, assuming that the
% series starts at 1.5.

% Copyright 2015 The MathWorks, Inc.

T = 100;
ARMdl = arima('AR',0.5,'Constant',0,'Variance',1);
x0 = 1.5;
rng(1); % For reproducibility
x = simulate(ARMdl,T,'Y0',x0);
%%
% Suppose further that the latent process is subject to additive
% measurement error.  Subsequently, the observation equation is
%
% $$y_t = x_t + \varepsilon_t,$$
%
% where $\varepsilon_t$ is Gaussian with mean 0 and standard deviation
% 0.75.  Together, the latent process and observation equations compose a
% state-space model. 

%%
% Use the random latent state process (|x|) and the observation equation to
% generate observations.
y = x + 0.75*randn(T,1);
%%
% Specify the four coefficient matrices.
A = 0.5;
B = 1;
C = 1;
D = 0.75;
%%
% Specify the state-space model using the coefficient matrices.
Mdl = ssm(A,B,C,D)
%%
% |Mdl| is an |ssm| model.  Verify that the model is correctly specified
% using the display in the Command Window. The software
% infers that the state process is stationary.  Subsequently, the
% software sets the initial state mean and covariance to the mean and
% variance of the stationary distribution of an AR(1) model.
%%
% Estimate the filtered states for periods 1 through 100.  Plot the true
% state values and the estimated, filtered states.
filteredX = filter(Mdl,y);

figure
plot(1:T,x,'-k',1:T,filteredX,':r','LineWidth',2)
title({'State Values'})
xlabel('Period')
ylabel('State')
legend({'True state values','Filtered state values'})
%%
% The true values and filter estimates are approximately the same.