Boosting the Hodrick-Prescott Filter

46 Pages Posted: 5 Sep 2019

See all articles by Peter C. B. Phillips

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Zhentao Shi

Department of Economics, the Chinese University of Hong Kong

Date Written: May 1, 2019

Abstract

The Hodrick-Prescott (HP) filter is one of the most widely used econometric methods in applied macroeconomic research. The technique is nonparametric and seeks to decompose a time series into a trend and a cyclical component unaided by economic theory or prior trend specification. Like all nonparametric methods, the HP filter depends critically on a tuning parameter that controls the degree of smoothing. Yet in contrast to modern nonparametric methods and applied work with these procedures, empirical practice with the HP filter almost universally relies on standard settings for the tuning parameter that have been suggested largely by experimentation with macroeconomic data and heuristic reasoning about the form of economic cycles and trends. As recent research has shown, standard settings may not be adequate in removing trends, particularly stochastic trends, in economic data. This paper proposes an easy-to-implement practical procedure of iterating the HP smoother that is intended to make the filter a smarter smoothing device for trend estimation and trend elimination. We call this iterated HP technique the boosted HP filter in view of its connection to L_2-boosting in machine learning. The paper develops limit theory to show that the boosted HP filter asymptotically recovers trend mechanisms that involve unit root processes, deterministic polynomial drifts, and polynomial drifts with structural breaks – the most common trends that appear in macroeconomic data and current modeling methodology. In doing so, the boosted filter provides a new mechanism for consistently estimating multiple structural breaks. A stopping criterion is used to automate the iterative HP algorithm, making it a data-determined method that is ready for modern data-rich environments in economic research. The methodology is illustrated using three real data examples that highlight the differences between simple HP filtering, the data-determined boosted filter, and an alternative autoregressive approach. These examples show that the boosted HP filter is helpful in analyzing a large collection of heterogeneous macroeconomic time series that manifest various degrees of persistence, trend behavior, and volatility.

Keywords: Boosting, Cycles, Empirical macroeconomics, Hodrick-Prescott filter, Machine learning, Nonstationary time series, Trends, Unit root processes

JEL Classification: C22, C55, E20

Suggested Citation

Phillips, Peter C. B. and Shi, Zhentao, Boosting the Hodrick-Prescott Filter (May 1, 2019). Cowles Foundation Discussion Paper No. 2192, May 2019, Available at SSRN: https://ssrn.com/abstract=3447546 or http://dx.doi.org/10.2139/ssrn.3447546

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

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Yale University - Cowles Foundation ( email )

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New Haven, CT 06520-8281
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Singapore Management University - School of Economics

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178903
Singapore

Zhentao Shi

Department of Economics, the Chinese University of Hong Kong ( email )

Shatin, N.T.
Hong Kong

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