Why we should use high values for the smoothing parameter of the Hodrick-Prescott filter

The HP filter is the most popular filter for extracting the trend and cycle components from an observed time series. Many researchers consider the smoothing parameter lambda = 1600 as something like an 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 one gets 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.