Characteristic period analysis of the Chinese stock market using successive one-sided HP filter

Time series of stock indices usually exhibit nonstationary and chaotic behavior. Analysis of the characteristics of the business cycle can reveal pertinent insights into the evolution of the stock volatility. This paper studies the characteristic periods of three main Chinese stock indices, i.e., the Shanghai composite index (SHCI), the Shenzhen component index (SZCI), and the Hang Seng index (HSI). We propose an approach based on the successive one-sided Hodrick-Prescott (SOHP) filtering and wavelet analysis of the empirical data from the stock markets, to detect their characteristic periods. In particular, the SOHP filter, which preprocesses the time series with a moving-horizon optimization procedure, enables us to extract the volatility cycles in different time scales from a stock time series and reduce noise distortion. The characteristic period of the stock index is then determined by the maxima of the wavelet power spectrum of the filtered data. The evolution of the characteristic period in time demonstrates rich information concerning the period stability of the stock market, as well as the cause and effect of the stock crash. To facilitate solving the moving-horizon optimization issue of the SOHP filter, we also present an incremental HP filtering algorithm, which greatly simplifies the involved inverse matrix operation in the HP-type filters.