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

TL;DR

This paper introduces a successive one-sided Hodrick-Prescott filter with an incremental algorithm for improved trend estimation in nonlinear economic time series, enhancing computational efficiency and performance.

Contribution

The paper presents a novel recursive SOHP filter and an incremental HP filtering algorithm that simplifies computations and improves trend extraction for large or expanding datasets.

Findings

Better trend estimation performance on real economic data.

Reduced computational complexity compared to traditional HP filtering.

Effective application to large-scale and expanding data scenarios.

Abstract

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