Scoring Six Detrending Methods on Timing, Lead‑Lag Relations, and Cycle Periods: An Empirical Study of US and UK Recessions 1977–2020

Abstract

This study evaluates six commonly used detrending methods and discuss how detrending may change the timing of events, the identification of lead-lag relations between GDP and employment, and the identification of cycle periods. The detrending methods examined includes linear detrending, polynomial detrending, the first-order differencing, locally weighted scatterplot smoothing (LOESS), Hodrick–Prescott filter, and the Hamilton filter. We apply the detrending methods to the United States and United Kingdom gross domestic product (GDP) from 1977 to 2020. We find that for the GDP series the first-order differencing score best on all three criteria, however, it also shows more false recessions than the other detrending methods. A linear, a polynomial, and a LOESS trend all scored well. The three methods miss-specified the timing of the recessions with less than one quarter and all three gave results that would comply with stylized facts in macroeconomics. The Hodrick–Prescott (HP) filter and Hamilton filter did not achieve high scores on one or two of the criteria and scored worst on average performance.