On Adjusting the One‐Sided Hodrick–Prescott Filter

We show that one should not use the one‐sided Hodrick–Prescott (HP‐1s) filter as the real‐time version of the two‐sided HP (HP‐2s) filter: First, in terms of the extracted cyclical component, HP‐1s fails to remove low‐frequency fluctuations to the same extent as HP‐2s. Second, HP‐1s dampens fluctuations at all frequencies—even those it is meant to extract. As a remedy, we propose two small adjustments to HP‐1s, aligning its properties closely with those of HP‐2s: (i) a lower value for the smoothing parameter and (ii) a multiplicative rescaling of the extracted cyclical component. For example, for HP‐2s with λ=1,600$\lambda = 1,600$ (value of smoothing parameter), the adjusted one‐sided HP filter uses λ∗=650$\lambda ^* = 650$ and rescales the extracted cyclical component by a factor of 1.1513. Using simulated and empirical data, we illustrate the relevance of these adjustments. For instance, financial cycles may appear to be 72% more volatile than business cycles, where, in fact, volatilities differ only marginally.