A Novel Tree-Based Combined Test for Seasonality

Conducting routine seasonal adjustments of economic data has been an important responsibility of federal statistical agencies for decades. Since those adjustments typically include regular checks for the presence of seasonality in a given series, most seasonal adjustment programs contain multiple seasonality tests plus an overall test that condenses their outcomes into an unambiguous decision to resolve any disagreement. However, key design elements of such overall tests—ensemble members, testing order and significance thresholds—often reflect the designer’s experience and/or preferences and hence might lack solid footing on rigorous statistical concepts. For that reason, we show how conditional inference trees can be used to devise more sophisticated alternatives. Treating the detection of seasonality as a classification problem and the tests’ p-values as correlated predictors, the first step is to identify the most important tests in the ensemble via recursive feature elimination in multiple random forests of such trees; the second step is to grow and prune a single tree based upon information from only these identified tests. We use simulated data to demonstrate that an ensemble of 15 seasonality diagnostics can be reduced to a low-complexity combination of three tests that has significantly lower misclassification rates than competing well-established overall tests.