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 type of seasonal model for the autocovariances is a more involved issue. 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 (DFT) is used to check estimates of the series’ frequency increments for periodic correlation. Asymptotic results are proven and the methods are illustrated with applications to two economic series.
