Indicator Saturation

Traditionally, the analysis of outliers and structural breaks in regression analysis was conducted by testing the statistical significance of a parsimonious, predetermined set of related indicator variables. More recently, advances in computing power and the development of general-to-specific (GETS) modeling permit testing of indicators at each observation in the estimation sample.

The indicator saturation approach is an extension of least squares regression for testing for outliers and structural breaks in a regression specification. The indicator saturation approach works by including indicator variables for outliers or structural breaks at every observation in the regression, and then employing the GETS algorithms to select which of the included variables should be retained in a final regression model.

Note that inclusion of indicators at each observation would ordinarily be prohibited due to the singularity of the regressor matrix, but the introduction of block estimation in GETS modeling
“Auto-Search / GETS”, allows testing of indicators throughout the estimation sample.

In EViews, you may perform indicator saturation on simple linear equations (which do not include ARMA terms) estimated using least squares. EViews offers testing for three different indicator types at each period t:

• Impulse Indicators (IIS): a dummy variable equal to zero everywhere other than a single value of one at period t. This indicator is equivalent to the @isperiod function used at the date corresponding to t.

• Step Indicators (SIS): a step function variable equal to zero until t and one thereafter. This indicator is equivalent to the @after function used at the date corresponding to t.

• Trend Indicators (TIS): a trend-break variable that is equal to zero until period t and then a follows a trend afterward. This indicator is equivalent to the @trendbr function used at the date corresponding to t.

(Note that an SIS indicator at t and is numerically the same as an IIS indicator at t. Similarly, a TIS indicator at t and is numerically identical to an SIS indicator at t. For this reason, when testing for these combinations of indicators, EViews will automatically drop the numerically equivalent variables.)

To instruct EViews to detect indicators in your least squares regression, open the equation estimation dialog, enter your least squares specification in the Equation specification edit field, and select LS - Least Squares (NLS and ARMA) in the Method dialog. Next, click on the Options tab to display the dialog:

Select the Auto-detect check box in the Outlier/indicator saturation area on the right-hand side of the dialog, and then press the Options tab to bring up the Indicator Options dialog:

There are a number of settings which control the indicator saturation analysis:

• The Indicator types section allows you to specify which type of indicator you would like to detect. You may individually choose to test for Impulse (IIS), Step-shift (SIS), and Trend (TIS) indicators by selecting the corresponding checkbox.

• In the Model selection area, the Criterion dropdown specifies the information criteria used to select the final model from the candidate models. The Include empty model check box specifies whether to the empty model (with no indicators) as possible a possible candidate model.

• The Sample edit field in the Variable creation area allows you to specify a different set of dates over which to create the indicators. By default, the estimation sample is used, but you may enter a different sample if desired.

• The Blocks edit field allows you to specify the number of blocks the indicators will be split into. Since the number of indicators will exceed the number of observations, indicators will be added in blocks. EViews will automatically determine the optimal number of blocks, but you may enter your own choice in this field to override the EViews default.

The Chronological blocking and Alternating blocking radio buttons determine whether the indicators are split into blocks in chronologically (the first group of dates in the first block, followed by the next group in the second block and so on), or alternating (the first date in the first block, second date in the second block and so on).

• The Diagnostics set of options allows selection of which indicator saturation diagnostic tests to include along with their p-values. You may perform AR LM (autoregressive LM), ARCH LM, Normality, and the PET (Parsimonius Encompassing Test) testing. For the AR LM test and ARCH LM test, you should specify the number of lags to include.

Once an equation has been estimated with indicator saturation variables, a new post-estimation diagnostic is available from the View menu. Select View/Indicator Summary to display a summary of the indicators that were included, and, if any were detected, produces a chart of the trajectory of the indicators through time.