MATLAB Examples

Specify ARIMAX Model Using Name-Value Pairs

This example shows how to specify an ARIMAX model using arima.

Specify the ARIMAX(1,1,0) model that includes three predictors:

$$(1 - 0.1L){(1 - L)^1}{y_t} = x_t^\prime {\left[ {\begin{array}{*{20}{c}}3&{ - 2}&5\end{array}} \right]^\prime } + {\varepsilon _t}.$$

model = arima('AR',0.1,'D',1,'Beta',[3 -2 5])
model = 

    ARIMAX(1,1,0) Model:
    ---------------------
    Distribution: Name = 'Gaussian'
               P: 2
               D: 1
               Q: 0
        Constant: NaN
              AR: {0.1} at Lags [1]
             SAR: {}
              MA: {}
             SMA: {}
            Beta: [3 -2 5]
        Variance: NaN

The output shows that the ARIMAX model, model, has the following qualities:

  • Property P in the output is the sum of the autoregressive lags and the degree of integration, i.e., P = p + D = 2.
  • Beta contains three coefficients corresponding to the effect that the predictors have on the response.
  • The rest of the properties are 0, NaN, or empty cells.

Be aware that if you specify nonzero D or Seasonality, then Econometrics Toolbox™ differences the response series $y_t$ before the predictors enter the model. Therefore, the predictors enter a stationary model with respect to the response series $y_t$. You should preprocess the predictors $x_t$ by testing for stationarity and differencing if any are unit root nonstationary. If any nonstationary predictor enters the model, then the false negative rate for significance tests of $\beta$ can increase.