ARMAX Modeling

ARMAX is essentially a linear regression model that uses an ARMA-type model for residuals. The input time series and the exogenous variables must be either all stationary or cointegrated.

The ARMAX Model Wizard in NumXL automates the model construction steps: guessing initial parameters, parameters validation, the goodness of fit testing, and residuals diagnosis.

Process

To use this functionality, select an empty cell in your worksheet and locate/select the ARMAX icon on the toolbar (or the menu item):

The NumXL ARMAX Model Wizard pops up.

By default, the output is set to reference the active cells on your worksheet. Next, select or point to the cells range where you store the input (dependent) data sample and the exogenous (explanatory/independent) variables on your worksheet.

Once you select the input data, the “Model” and “Options” tabs are enabled. Click the “Model” tab now.

For ARMAX, we will keep the “Seasonal” checkbox unchecked and set the non-seasonal integration order to zero (default). Select the corresponding order of the auto-regressive (AR) component model and the order of the moving-average component model.

Now, click on the “Options” tab.

On this tab, we can instruct the Model Wizard on whether to generate goodness of fit and residual diagnosis tables. We can also determine how it should initialize the values of the model’s parameters, with either a quick guess or calibrated optimal values.

Output

Upon completion, the ARMAX modeling function outputs the selected model's parameters and selected tests/calculations in the designated location of your worksheet.