BUSINESS CYCLES, TREND ELIMINATION, AND THE HP FILTER

By Peter C. B. Phillips, Sainan Jin. International Economic Review, 2020

99 citations recorded by the source corpus.

We analyze trend elimination methods and business cycle estimation by data filtering of the type introduced by Whittaker (1923) and popularized in economics in a particular form by Hodrick and Prescott (1980/1997; HP). A limit theory is developed for the HP filter for various classes of stochastic trend, trend break, and trend stationary data. Properties of the filtered series are shown to depend closely on the choice of the smoothing parameter (lambda). For instance, when lambda = O(n^4) where n is the sample size, and the HP filter is applied to an I(1) process, the filter does not remove the stochastic trend in the limit as n approaches infinity. Instead, the filter produces a smoothed Gaussian limit process that is differentiable to the 4'th order. The residual 'cyclical' process has the random wandering non-differentiable characteristics of Brownian motion, thereby explaining the frequently observed 'spurious cycle' effect of the HP filter. On the other hand, when lambda = o(n), the filter reproduces the limit Brownian motion and eliminates the stochastic trend giving a zero 'cyclical' process. Simulations reveal that the lambda = O(n^4) limit theory provides a good approximation to the actual HP filter for sample sizes common in practical work. When it is used as a trend removal device, the HP filter therefore typically fails to eliminate stochastic trends, contrary to what is now standard belief in applied macroeconomics. The findings are related to recent public debates about the long run effects of the global financial crisis.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/4a48c34a6df279e2bd0d5576a888190ce968d5cd

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Citations in the corpus

• DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection (2023, methodology): “Statistical methods include using moving averages, exponential smoothing [53], and the autoregressive integrated moving average (ARIMA) model [9].”