Estimating Periodic Length and Phase Shifts of Business Cycles: An Approach from Model-based Uni- and Multi-variate Bandpass Filter(in Japanese)

This paper verified possible application of model-based univariate and multivariate Bandpass filter for Japanese time series data. Firstly, we extracted cycle components and estimated periodic length of monthly univariate time series such as coincident index (CCI) and the index of industrial production (IIP) using Generalized Butterworth Filter, a kind of unobservable component models, following Harvey and Trimbur (2003). The feature of the method is to estimate the parameters of models from actual data, unlike HP filter and Baxter-King Filter. Secondly, we turned to estimate phase shifts of multivariate time series such as inventoryproduction diagram and leading, coincident and lagged series using Multivariate Bandpass filter following Valla e Azevedo, Koopman and Rua (2006). The advantage of the method is to extract common cycle component from multivariate series even with phase shifts among them, whereas earlier methods can do it for only univariate series.