MATLAB Examples

AR Model with a t Innovation Distribution

This example shows how to specify an AR($p$) model with a Student's t innovation distribution.

Specify an AR(2) model with no constant term,

$${y_t} = {\phi _1}{y_{t - 1}} + {\phi _2}{y_{t - 2}} + {\varepsilon _t},$$

where the innovations follow a Student's t distribution with unknown degrees of freedom.

model = arima('Constant',0,'ARLags',1:2,'Distribution','t')
model = 

    ARIMA(2,0,0) Model:
    Distribution: Name = 't', DoF = NaN
               P: 2
               D: 0
               Q: 0
        Constant: 0
              AR: {NaN NaN} at Lags [1 2]
             SAR: {}
              MA: {}
             SMA: {}
        Variance: NaN

The value of Distribution is a struct array with field Name equal to 't' and field DoF equal to NaN. The NaN value indicates the degrees of freedom are unknown, and need to be estimated using estimate or otherwise specified by the user.