Business Cycle Estimation with High-Pass and Band-Pass Local Polynomial Regression

Luis Álvarez

doi:10.3390/econometrics5010001

Abstract

Filters constructed on the basis of standard local polynomial regression (LPR) methods have been used in the literature to estimate the business cycle. We provide a frequency domain interpretation of the contrast filter obtained by the difference of a series and its long-run LPR component and show that it operates as a kind of high-pass filter, so that it provides a noisy estimate of the cycle. We alternatively propose band-pass local polynomial regression methods aimed at isolating the cyclical component. Results are compared to standard high-pass and band-pass filters. Procedures are illustrated using the US GDP series.

Highlights

There is a large body of literature on methods to estimate the business cycle [1,2,3,4] and the GreatRecession has rekindled the interest in business cycle analysis
Local polynomial regression [5,6,7,8] is a well-known method in the statistical literature, which has been used for business cycle analysis [9]
As shown in the results section below, local polynomial regression-based methods for business cycle analysis operate as a kind of high-pass filter, so in the comparisons below we compare them to an ideal high-pass filter

Summary

Introduction

There is a large body of literature on methods to estimate the business cycle [1,2,3,4] and the Great. The underlying idea of this nonparametric method is that any function can be well approximated by a Taylor series expansion in the neighborhood of any point This smooth function is a natural estimator of the low frequency (long-run) component of the series (i.e., the trend or the trend-cycle component). The resulting component is obtained by a kind of high-pass filter, so that it provides an estimate of the cycle (plus short-run noise) The aim of this communication is to assess the validity of local polynomial regression-based methods for business cycle analysis. We provide a frequency domain interpretation of cyclical filters obtained on the basis of standard local polynomial regression methods, taking different assumptions about the bandwidths and kernels functions, and show that they act as a kind of high-pass filters so that they result in noisy cycles.

Materials and Methods

Band-Pass Local Polynomial Regression

High-Pass Local Polynomial Regression

Empirical Applications

Results

Band-Pass