Hyper-trend method for seasonal adjustment and trend-cycle decomposition of time series containing long-period cycles

Abstract

In some instances, existing methods for decomposing a time series into several components cannot capture cyclical components that contain long-period cycles. We propose a systematic methodology to overcome this problem. In the proposed hyper-trend method, we assume that part of the cyclical variation is included in the estimate of the trend component. We then capture the remainder of the cyclical variation by re-decomposing the estimate of the trend component. The average coefficient of determination is introduced to evaluate the decomposed results. An overall procedure for applying the proposed approach is developed, and the performance of the proposed approach is demonstrated by analysing 20 commercial sales time series and 30 business cycle time series.