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Business Cycles, Trend Elimination, And The Hp Filter

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  • Peter C. B. Phillips
  • Sainan Jin

Abstract

Trend elimination and business cycle estimation are analyzed by finite sample and asymptotic methods. An overview history is provided, operator theory is developed, limit theory as the sample size n→∞ is derived, and filtered series properties are studied relative to smoothing parameter (λ) behavior. Simulations reveal that limit theory with λ=O(n4) delivers excellent approximations to the HP filter for common sample sizes but fails to remove stochastic trends, contrary to standard thinking in macroeconomics and thereby explaining “spurious cycle” effects of the HP filter. The findings are related to the long run effects of the global financial crisis.

Suggested Citation

  • Peter C. B. Phillips & Sainan Jin, 2021. "Business Cycles, Trend Elimination, And The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 469-520, May.
    • Handle: RePEc:wly:iecrev:v:62:y:2021:i:2:p:469-520
    DOI: 10.1111/iere.12494
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    6. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
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    9. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
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    23. Shiller, Robert J, 1973. "A Distributed Lag Estimator Derived from Smoothness Priors," Econometrica, Econometric Society, vol. 41(4), pages 775-788, July.
    24. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
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    26. Cogley, Timothy & Nason, James M., 1995. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 253-278.
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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