The boosted HP filter is more general than you might think

TL;DR

This paper demonstrates that the boosted Hodrick-Prescott filter is a versatile and powerful method for trend-cycle analysis in macroeconomic data, capable of handling complex time series with local to unity roots.

Contribution

It extends boosting's trend detection to higher order integrated processes and local to unity roots, supported by theoretical analysis and empirical application.

Findings

Boosted HP filter effectively captures downturns and recoveries in macroeconomic data.

Theoretical analysis shows asymptotic properties of boosting on exponential functions.

Empirical results from FRED data demonstrate improved trend detection.

Abstract

The global financial crisis and Covid recession have renewed discussion concerning trend-cycle discovery in macroeconomic data, and boosting has recently upgraded the popular HP filter to a modern machine learning device suited to data-rich and rapid computational environments. This paper extends boosting's trend determination capability to higher order integrated processes and time series with roots that are local to unity. The theory is established by understanding the asymptotic effect of boosting on a simple exponential function. Given a universe of time series in FRED databases that exhibit various dynamic patterns, boosting timely captures downturns at crises and recoveries that follow.