Reconsidering Hodrick-Prescott Detrending and Its Smoothing Parameter : Extended Version

The paper reconsiders the Hodrick-Prescott filter and the issue of a suitable choice of its smoothing parameter λ for quarterly data. To this end stochastic processes generate artificial data with a known growth trend and cyclical component, and a battery of Monte Carlo experiments tests what values of λ yield the best approximation of the true trend. Specifically, the main summary statistics of the first differences of the data are required to come close to those of the real gross value added in the US, while the average length of their cyclical fluctuations is largely compatible with the spectograms of other business cycle data. Regarding the trend component, it proves to be important to distinguish between a deterministic and stochastic trend. Generally it is found that good values of λ are seven to twelve times higher than the conventional λ = 1600. Since it may for certain purposes be more intuitive, the paper also offers a slight modification of the filter that now results in a segmented linear trend. Suitable values of the tuning parameter that determines the endogenous break points are obtained from the same experiments. In comparison, it turns out that this procedure is on average marginally superior (inferior) if a deterministic (stochastic) trend is underlying. After settling down on a recommendation for suitable parameter values and a check of their robustness, it is finally shown that the main summary statistics of the estimated cyclical component exhibit a small downward bias