Seasonal Autocovariance Structures: PARMA or SARMA?

• Activity Number: 480
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Robert Lund*+
• Companies: Clemson University
• Keywords: PARMA ; SARMA ; Spectral Analysis ; Autocorrelation ; Seasonality

Abstract

Many time series have some type of seasonality (periodicity) in their first two moments. While seasonality in the first moment is typically removed by differencing at the seasonal lag (or estimated and removed by subtracting periodic sample means), selecting the appropriate seasonal autocovariance model is more involved. Here, we present a simple test to assess whether a periodic autoregressive moving-average (PARMA) model is preferred to a seasonal autoregressive moving-average (SARMA) model. The test can be used to check for periodic variances (periodic heteroskedasticity) or periodic autocorrelations. The methods are developed in the frequency domain, where the discrete Fourier transform is used to check estimates of the series' frequency increments for periodic correlation. The methods are illustrated with applications to two economic series; in both cases, a PARMA structure is preferred.