Journal of Economic Dynamics and Control
Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research
Timothy Cogley a, James M. Nason b
aResearch Department, Federal Reserve Bank of San Francisco, San Francisco, CA 94120, USA
b Department of Economics, University of British Columbia, Vancouver, B. C., V6T 1Z1, Canada
(Received April 1993; final version received September 1993)
When applied to persistent time series, the Hodrick-Prescott filter can generate business cycle dynamics even if none are present in the original data. Hence the presence of business cycles in HP filtered data does not imply that there are business cycles in the original data. For example, we show that standard real business cycle models do not generate business cycle dynamics in pre-filtered data and that the business cycles observed in HP filtered data are due to the filter. As another example, we show that under plausible assumptions HP stylized facts are determined primarily by the filter and reveal little about the dynamics of the underlying data.
Key words: Business fluctuations; Time series models; Model evaluation and testing JEL classification: E32; C22; C52
Macroeconomic time series often have an upward drift or trend which makes them nonstationary. Since many statistical procedures assume stationarity, it is
* Corresponding author.
We thank Roger Craine, Jon Faust, Andrew Harvey, Stephen LeRoy, Charles Nelson, Adrian Pagan, Kenneth West, and a referee for helpful comments. Much of this research was done while Cogley was visiting the Haas School of Business at U. C. Berkeley, and their hospitality is gratefully acknowledged. Opinions expressed in this paper do not necessarily represent the views of the Federal Reserve Bank of San Francisco or the Federal Reserve System.
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