Building confidence intervals for band-pass and Hodrick–Prescott filters: an application using bootstrapping

Abstract

This article generates innovative confidence intervals for two of the most popular de-trending methods: Hodrick–Prescott and band-pass filters. The confidence intervals are obtained using block-bootstrapping techniques for dependent data. GDP trend growth and output gap intervals for the G7 economies are used as examples. This new methodology increases the usefulness of these filters by overcoming the absence of confidence intervals.

Acknowledgements

We thank Rómulo Chumacero, Klaus Schmidt-Hebbel, and an anonymous referee for helpful comments. This paper was written while both authors were affiliated with the Central Bank of Chile.

Notes

Although this study was published in 1997, the original draft, which is widely cited, was written in 1980.

Recent studies present sophisticated methods for finding the optimal window for any time series, adjusting for data frequency (Ravn and Uhlig, 2001).

For an analysis of adjusting the HP Filter depending on the data frequency, see Ravn and Uhlig (2001).