Complementary Properties of an F-Test and an Empirical Spectral Test for Identifying Seasonality in Unadjusted or Seasonally Adjusted Series

• Activity Number: 450
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): David Findley*+
• Companies: U.S. Census Bureau
• Keywords: Seasonal adjustment ; Residual seasonality ; Seasonality diagnostics ; Stationary seasonality ; X-13ARIMA-SEATS

Abstract

We compare the AR spectrum test of X-12-ARIMA and the stable seasonal F-test of Lytras, Feldpausch and Bell (2007), who demonstrated that the latter is well-sized and the former substantially oversized when testing at the .05 level. In contrast, we present results from simulations of stationary seasonal ARMA models with a seasonal AR coefficient of THETA12=0.4 or less and show the F-test incorrectly identifies stable seasonality in the majority of these series, whereas the spectrum test rarely makes this error. We also explain why the spectrum test, limited by default to the last 96 months of data, much more readily identifies residual seasonality in poorly adjusted time series with moving seasonality than the F-test and show that, at the expense of a second run of the software on the last 108 months of the seasonally adjusted series considered, the F-test becomes competitive.