242 – Time Series: Autoregressive Processes, Seasonality, and Unit Roots
On Seasonality: Comparing X-13ARIMA-SEATS Diagnostics for Quarterly Series
Demetra Lytras
U.S. Census Bureau
X-13ARIMA-SEATS has several diagnostics for determining whether an original time series is seasonal and for detecting residual seasonality in an adjusted series. However, seasonality diagnostics are more limited for quarterly series, as the spectrum diagnostic is available only for monthly series. Familiar diagnostics that are available for quarterly series either apply only to x11 adjustments and not to SEATS adjustments or require an additional run. X-13ARIMA-SEATS's newest seasonality diagnostics are the QS statistics, which were first available in the Bank of Spain's SEATS software. They measure positive seasonal autocorrelation in the original and adjusted series and are available for both monthly and quarterly, x11 and SEATS adjustments. This paper compares their efficacy in finding seasonality to that of the spectrum, the F test of seasonal regressors, and various x11 diagnostics using both real U.S. Census Bureau series and simulated seasonal and nonseasonal series.