On the Hamilton-HP Filter Controversy: Evidence from German Business Cycles

Abstract

James Hamilton put doubt on the quality of the HP filter estimates, and proposed an alternative regression approach to decompose trend and cycle of time series (H filter). We investigate the new H filter in detail and compare it to the HP filter. We apply both to German GDP time series. We find that in times of huge shocks the regular H filter produces unreliable trends. Its Quast-Wolters modification (QWH filter), in contrast, does not suffer from this issue. Checking expert benchmark congruency, we find that this modification outperforms all parameter constellations of the standard H filter. With a benchmark-specific adequate choice of the smoothing factor, in turn, the HP filter outperforms the H filter. The H filter, however, outperforms the HP filter with regard to correlation with expert benchmark recession dating. And the H filter uniquely outperforms the HP filter in capturing the gap-inflation link, an issue especially important for central banks. Overall, our results suggest using the QWH filter among the H filter options, and a smoothing factor of 38 for the HP filter.