Open Access Article

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

Authors: Koki Kyo; Genshiro Kitagawa

Addresses: Faculty of Management and Information Science, Niigata University of Management, Kamo-shi, Niigata, Japan ' Mathematics and Informatics Center, Tokyo University, Bunkyo-ku, Tokyo, Japan; Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano-ku, Tokyo, Japan

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.

Keywords: seasonal adjustment; trend-cycle decomposition; hyper-trend method; state space model; Kalman filter; economic time series; commercial sales; business cycles; DECOMP; stationarity of a time series.

DOI: 10.1504/AJMSA.2021.120434

Asian Journal of Management Science and Applications, 2021 Vol.6 No.2, pp.134 - 162

Received: 10 Jun 2021
Accepted: 16 Sep 2021

Published online: 19 Jan 2022 *