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We propose a successive one-sided Hodrick-Prescott (SOHP) filter frommultiple time scale decomposition perspective to derive trend estimate for atime series. The idea is to apply the one-sided HP (OHP) filter recursively onthe updated cyclical component to extract the trend residual on multiple timescales, thereby to improve the trend estimate. To address the issue ofoptimization with a moving horizon as that of the SOHP filter, we present anincremental HP filtering algorithm, which greatly simplifies the involvedinverse matrix operation and reduces the computational demand of the basic HPfiltering. Actually, the new algorithm also applies effectively to otherHP-type filters, especially for large-size or expanding data scenario.Numerical examples on real economic data show the better performance of theSOHP filter in comparison with other known HP-type filters.

Successive one-sided Hodrick-Prescott filter with incremental filtering algorithm for nonlinear economic time series