Cycle Extraction: A Comparison of the Phase-Average Trend Method, the Hodrick-Prescott and Christiano-Fitzgerald Filters

This paper reports on revision properties of different de-trending and smoothing methods (cycle estimation methods), including PAT with MCD smoothing, a double Hodrick-Prescott (HP) filter and the Christiano-Fitzgerald (CF) filter. The different cycle estimation methods are rated on their revision performance in a simulated real time experiment. Our goal is to find a robust method that gives early turning point signals and steady turning point signals. The revision performance of the methods has been evaluated according to bias, overall revision size and signal stability measures. In a second phase, we investigate if revision performance is improved using stabilizing forecasts or by changing the cycle estimation window from the baseline 6 and 96 months (i.e. filtering out high frequency noise with a cycle length shorter than 6 months and removing trend components with cycle length longer than 96 months) to 12 and 120 months. The results show that, for all tested time series, the PAT de-trending method is outperformed by both the HP or CF filter. In addition, the results indicate that the HP filter outperforms the CF filter in turning point signal stability but has a weaker performance in absolute numerical precision. Short horizon stabilizing forecasts tend to improve revision characteristics of both methods and the changed filter window also delivers more robust turning point estimates.