Constructing confidence bands for the Hodrick–Prescott filter

Abstract

By noting that the Hodrick–Prescott (H–P) filter can be used as the solution to a particular regression problem, we are able to show how to construct confidence bands for the filtered time-series. This procedure requires that the data are stationary. The construction of such confidence bands is illustrated using annual US data for real value-added output and monthly US data for the unemployment rate.

Keywords:

• Hodrick–Prescott filter
• time-series decomposition
• confidence bands

JEL Classification:

• C13
• C20
• E3

Acknowledgements

I am grateful to Riccardo (Jack) Luccetti and Graham Voss for their helpful comments on an informal earlier version of this work.