On Adjusting the HP-Filter for the Frequency of Observations

Abstract

This paper studies how the HP-Filter should be adjusted, when changing the frequency of observations. The usual choices in the literature are to adjust the smoothing parameter by multiplying it with either the square of the observation frequency ratios or simply with the observation frequency. In contrast, the paper recommends to adjust the filter parameter by multiplying it with the fourth power of the observation frequency ratios. Based on this suggestion, some well-known comparisons of business cycles moments across countries and time periods are recomputed. In particular, we overturn a finding by Backus and Kehoe (1992) on the historical changes in output volatility and return instead to older conventional wisdom (Baily, 1978, Lucas, 1977): based on the new HP-Filter adjustment rule, output volatility turns out to have decreased after the Second World War.