Selection and Estimation of Trigonometric Component Models for Seasonal Time Series

Abstract

We present a method for investigating the evolution of trend and seasonality in an observed time series. A general model is fitted to a residual spectrum, using trigonometric components to represent the seasonality. We show graphically how well the fitted spectrum captures the evidence for evolving seasonality associated with the different seasonal frequencies. After fitting a seasonal IMA model, the method requires only ordinary least squares estimation. A submodel which adequately fits the data can then be conveniently selected. We apply the method to two time series and discuss the implications for time series forecasting