#### Title

Boosting: Why you Can Use the HP Filter

Discussion Paper

12-1-2019

2212

57

C22, C55, E20

#### 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 \citep{phillips2015business} 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 \emph{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 (bHP) ﬁlter asymptotically recovers trend mechanisms that involve unit root processes, deterministic polynomial drifts, and polynomial drifts with structural breaks, thereby covering 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 even without knowledge of the number of such 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 bHP ﬁlter is helpful in analyzing a large collection of heterogeneous macroeconomic time series that manifest various degrees of persistence, trend behavior, and volatility.

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