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

    %% ARMA Model  
% This example shows how to plot the impulse response function for an autoregressive
% moving average (ARMA) model. The ARMA(_p_, _q_) model is given by 
%
% $${y_t} = \mu  + \frac{{\theta (L)}}{{\phi (L)}}{\varepsilon _t},$$
%
% where $\theta(L)$  is a _q_-degree MA operator polynomial,  $(1 + {\theta
% _1}L +  \ldots  + {\theta _q}{L^q})$, and $\phi(L)$ is a _p_-degree AR
% operator polynomial, $(1 - {\phi _1}L -  \ldots  - {\phi _p}{L^p})$.
%
% An ARMA process is stationary provided that the AR operator polynomial is
% stable, meaning all its roots lie outside the unit circle. In this case,
% the infinite-degree inverse polynomial, $\psi (L) = {{\theta (L)}
% \mathord{\left/ {\vphantom {{\theta (L)} {\phi (L)}}} \right.
% \kern-\nulldelimiterspace} {\phi (L)}}$ , has absolutely summable
% coefficients, and the impulse response function decays to zero.

% Copyright 2015 The MathWorks, Inc.


%% Step 1. Specify an ARMA model. 
% Specify an ARMA(2,1) model with coefficients $\phi_1$ = 0.6, $\phi_2 = -0.3$, and $\theta_1 = 0.4$.  
modelARMA = arima('AR',{0.6,-0.3},'MA',0.4);  

%% Step 2. Plot the impulse response function. 
% Plot the impulse response function for 10 periods. 
impulse(modelARMA,10)