Time-series decomposition using the sinusoidal model

This paper empirically supports the hypothesis that a sinusoidal model can be used successfully to decompose time-series data into its components. Since the length of the seasonal cycle is known, this study documents how one makes use of this known length to infer characteristics of the more general non-seasonal cycle. By examining the ratios of the lengths of the longer to the shorter sine waves in the resulting fit of a sinusoidal model, one is able to determine which sine waves are estimating the same cycle and what the average length of that cycle is. A non-linear trend is estimated by adding a sine wave to the linear trend.