MATLAB Examples

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.


The impulse function decays in a sinusoidal pattern.