Why We Should Use High Values for the Smoothing Parameter of the Hodrick-Prescott Filter

Summary The HP filter is the most popular filter for extracting the unobserved trend and cycle components from a time series. Many researchers consider the smoothing parameter λ = 1600 as something like a universal constant. It is well known that the HP filter is an optimal filter under some restrictive assumptions, especially that the “cycle” is white noise. In this paper we show that we can get a good approximation of the optimal Wiener-Kolmogorov filter for autocorrelated cycle components by using the HP filter with a much higher smoothing parameter than commonly used. In addition, a new method - based on the properties of the differences of the estimated trend - is proposed for the selection of the smoothing parameter.