MATLAB Examples

MA Error Model with Nonconsecutive Lags

This example shows how to specify a regression model with MA errors, where the nonzero MA terms are at nonconsecutive lags.

Specify the regression model with MA(12) errors:

$$\begin{array}{l}{y_t} = c + {X_t}\beta  + {u_t}\\{u_t} = {\varepsilon _t} + {b_1}{\varepsilon _{t - 1}} + {b_{12}}{\varepsilon _{t - 12}}.\end{array}$$

Mdl = regARIMA('MALags',[1, 12])
Mdl = 

    ARIMA(0,0,12) Error Model:
    --------------------------
    Distribution: Name = 'Gaussian'
       Intercept: NaN
               P: 0
               D: 0
               Q: 12
              AR: {}
             SAR: {}
              MA: {NaN NaN} at Lags [1 12]
             SMA: {}
        Variance: NaN

The MA coefficients are at lags 1 and 12.

Verify that the MA coefficients at lags 2 through 11 are 0.

Mdl.MA'
ans =

  12x1 cell array

    {[NaN]}
    {[  0]}
    {[  0]}
    {[  0]}
    {[  0]}
    {[  0]}
    {[  0]}
    {[  0]}
    {[  0]}
    {[  0]}
    {[  0]}
    {[NaN]}

After applying the transpose, the software displays a 12-by-1 cell array. Each consecutive cell contains the corresponding MA coefficient value.

Pass Mdl and data into estimate. The software estimates all parameters that have the value NaN. Then estimate holds $b_2$ = $b_3$ =...= $b_{11}$ = 0 during estimation.