Testing for Visual Significance in Seasonally Adjusted Time Series

• Activity Number: 324
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Anindya Roy*+ and Tucker Sprague McElroy
• Companies: University of Maryland Baltimore County and U.S. Census Bureau
• Keywords: fixed bandwidth-ratio ; spectral density ; pivoal distribution ; peak measure

Abstract

Seasonal adjustment methods process and publish millions of time series across the world each month, and judgment of the adequacy relies heavily upon frequency domain diagnostics. In particular, peaks in the spectral density estimates of seasonally adjusted data are indicative of an inadequate adjustment. Spectral peaks are currently assessed in the X-12-ARIMA program via the methodology of visual significance, but this method lacks a rigorous statistical foundation. This paper provides such a foundation by providing measures of uncertainty for spectral peak measures, allowing for formal hypothesis testing. We proceed by developing fixed bandwidth-ratio asymptotics for taper-based spectral density estimates, where the frequencies are allowed to depend upon sample size. We also develop a peak measure based upon the spectral distribution function. Quantiles are obtained by simulation of the pivotal limiting distributions and the resulting methods are illustrated on economic time series.