Using Spectral Peaks to Detect Seasonality

Peaks in the spectrum of a stationary time series indicate the presence of periodic phenomena, such as seasonal and cyclical components. Extending the approach of McElroy and Holan (2009), this paper constructs nonparametric peak-estimators via windowing the periodogram with the same sinusoidal function used to define seasonal autocovariances. We also utilize a multiple testing procedure that controls the familywise error rate, as in Hochberg (1988) and McElroy and Holan (2009). The application of these methods is exceedingly simple, requiring only a few lines of computer code; therefore the method can be used to quickly evaluate series for residual seasonality. Simulation studies demonstrate the good size and power of the procedure, and an extensive data study further illustrates the method.