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Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?

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  • Alain Guay
  • Pierre Saint-Amant

Abstract

The authors assess the ability of the Hodrick-Prescott filter (HP) and the band-pass filter proposed by Baxter and King (BK) to extract the business-cycle component of macroeconomic time series by using two different definitions of the business-cycle component. First, they define that component to be fluctuations lasting no fewer than 6 and no more than 32 quarters; this is the definition of business-cycle frequencies used by Baxter and King. Second, they define the business-cycle component on the basis of a decomposition of the series into permanent and transitory components. The conclusions are the same in both cases. The filters perform adequately when the spectrum of the original series has a peak at business-cycle frequencies. When the spectrum is dominated by low frequencies, the filters provide a distorted business cycle. These findings suggest that the use of the HP and BK filters with series having the typical Granger shape is highly problematic.

Suggested Citation

  • Alain Guay & Pierre Saint-Amant, 2005. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Annals of Economics and Statistics, GENES, issue 77, pages 133-155.
  • Handle: RePEc:adr:anecst:y:2005:i:77:p:133-155
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    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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