A Review of Seasonal Adjustment Diagnostics

Summary Seasonal adjustment methods are used to process and publish thousands of time series across the world each month, and judgement of the adequacy relies heavily upon seasonal adjustment diagnostics. This paper discusses tests for the adequacy of a seasonal adjustment, first reviewing the broader background on tests for seasonality and then proceeding to four tests that are appropriate for stationary forms of seasonality. We contrast time‐domain and frequency‐domain approaches, focusing upon four diagnostics available in the seasonal adjustment literature (and software packages) and applying the methods to a large collection of public use time series. Each of the four tests is designed around a distinct formulation of seasonality, and hence, empirical performances differ; we compare and contrast the methods and include discussion on how diagnostic results can be used to improve faulty seasonal adjustments. Directions for future research, involving inverse partial autocorrelations and polyspectra, are also discussed, and the methodologies are supported by theoretical and simulation results.