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

ArXiv ID: 2306.12439 “View on arXiv”

Authors: Unknown

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.

Keywords: Hodrick-Prescott (HP) filter, time series decomposition, trend estimation, incremental filtering, economic data, Macro / Econometrics

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper is heavily mathematical, featuring matrix operations (Woodbury identity), derivations of incremental algorithms, and complexity analysis (O(l³) vs O(l²)). It also demonstrates empirical rigor by testing on real S&P 500 and Shanghai Composite data, comparing performance against established baselines (HP, bHP, OHP), and providing a visual time-consumption plot.

  flowchart TD
    A["Research Goal: Improve Trend Estimation for<br>Nonlinear Economic Time Series"] --> B["Key Methodology:<br>Successive One-Sided HP (SOHP) Filter"]
    B --> C["Incremental Filtering Algorithm<br>(Addressing Moving Horizon Optimization)"]
    C --> D["Data Inputs:<br>Real Economic Time Series"]
    D --> E["Computational Process:<br>Recursive Application of OHP Filter<br>on Cyclical Components"]
    E --> F["Key Findings/Outcomes:<br>Better Performance vs. Other HP-Type Filters<br>Reduced Computational Demand"]
    F --> G["Conclusion: Effective for Large/Expanding Data"]