Detrending and financial cycle facts across G7 countries: Mind a spurious medium term!

I show that the detrending of financial variables with the Hodrick and Prescott (1981, 1997) (HP) and band-pass filters leads to spurious cycles. I find that distortions become especially severe when considering medium-term cycles, i.e., cycles that exceed the duration of regular business cycles. In particular, these medium-term filters amplify the variances of cycles of duration around 20 to 30 years up to a factor of 204, completely cancelling out shorter-term fluctuations. This is important because it is common practice, and recommended under Basel III, to extract medium-term cycles using such filters; e.g., the HP filter with a smoothing parameter of 400,000. In addition, I find that financial cycle facts, i.e., differing amplitude, duration, and synchronisation of cycles in financial variables relative to cycles in GDP, are robust. For HP and band-pass filters, differences to GDP become marginal due to spurious cycles.