Series Diagnostic Tests

This section describes the diagnostic tests that are used to determine the kinds of forecasting models appropriate for a series.

The series diagnostics are a set of heuristics that provide recommendations on whether or not the forecasting model should contain a log transform, trend terms, and seasonal terms. These recommendations are used by the automatic model selection process to restrict the model search to a subset of the model selection list. (You can disable this behavior by using the Automatic Model Selection Options window.)

The tests that are used by the series diagnostics do not always produce the correct classification of the series. They are intended to accelerate the process of searching for a good forecasting model for the series, but you should not rely on them if finding the very best model is important to you.

If you have information about the appropriate kinds of forecasting models (perhaps from studying the plots and autocorrelations shown in the Series Viewer window), you can set the series diagnostic flags in the Series Diagnostics window. Select the YES, NO, or MAYBE values for the Log Transform, Trend, and Seasonality options in the Series Diagnostics window as you think appropriate.

The series diagnostics tests are intended as a heuristic tool only, and no statistical validity is claimed for them. These tests might be modified and enhanced in future releases of the Time Series Forecasting System. The testing strategy is as follows:

1. Log transform test. The log test fits a high-order autoregressive model to the series and to the log of the series and compares goodness-of-fit measures for the prediction errors of the two models. If this test finds that log transforming the series is suitable, the Log Transform option is set to YES, and the subsequent diagnostic tests are performed on the log transformed series.

2. Trend test. The resultant series is tested for presence of a trend by using an augmented Dickey-Fuller test and a random walk with drift test. If either test finds that the series appears to have a trend, the Trend option is set to YES, and the subsequent diagnostic tests are performed on the differenced series.

3. Seasonality test. The resultant series is tested for seasonality. A seasonal dummy model with AR(1) errors is fit and the joint significance of the seasonal dummy estimates is tested. If the seasonal dummies are significant, the AIC statistic for this model is compared to the AIC for and AR(1) model without seasonal dummies. If the AIC for the seasonal model is lower than that of the nonseasonal model, the Seasonal option is set to YES.