%% Autoregressive Model
% This example shows how to compute and plot the impulse response function for an autoregressive (AR) model. The AR(p) model is given by
% {y_t} = \mu  + \phi {(L)^{ - 1}}{\varepsilon _t},
% where \phi(L) is a p-degree AR operator polynomial, (1 - {\phi _1}L -  \ldots  - {\phi _p}{L^p}).
% An AR 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) = \phi {(L)^{ - 1}}, has absolutely summable coefficients, and the impulse response function decays to zero.
%% Step 1. Specify the AR model.
% Specify an AR(2) model with coefficients \phi_1 = 0.5 and \phi_2 = -0.75.

modelAR = arima('AR',{0.5,-0.75});

%
%% Step 2. Plot the impulse response function.
% Plot the impulse response function for 30 periods.

impulse(modelAR,30)

% The impulse function decays in a sinusoidal pattern.
% Copyright 2015 The MathWorks, Inc.