The band pass filter

Lawrence J. Christiano, Terry J. Fitzgerald*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

577 Scopus citations

Abstract

We develop optimal finite-sample approximations for the band pass filter. These approximations include one-sided filters that can be used in real time. Optimal approximations depend upon the details of the time series representation that generates the data. Fortunately, for US. macroeconomic data, getting the details exactly right is not crucial. A simple approach, based on the generally false assumption that the data are generated by a random walk, is nearly optimal. We use the tools discussed here to document a new fact: There has been a significant shift in the money-inflation relationship before and after 1960.

Original languageEnglish (US)
Pages (from-to)435-465
Number of pages31
JournalInternational Economic Review
Volume44
Issue number2
DOIs
StatePublished - May 1 2003

ASJC Scopus subject areas

  • Economics and Econometrics

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