Selecting a Boosted HP Filter for Growth Cycle Analysis Based on Maximising Sharpness

The boosted HP (bHP) trend filter iterates the standard HP filter until the resulting trend deviation is free of any stochastic trend with the latter determined by suitable stopping rules. Here the performance and properties of the bHP trend filter for growth cycle analysis are considered based on the time-invariant moving-average representation of the bHP filter in the body of the series. We propose alternative trend selection criteria based on a constant cut-off frequency and maximising sharpness. We find there is a strong case for selecting a bHP trend filter with an 8-year rather than a 10-year cut-off period, and that using a bHP filter with 2 iterations (twicing) or a sharpened HP filter is preferable to using the standard HP filter.