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Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter

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  • Schlicht, Ekkehart

Abstract

This note gives a fairly complete statistical description of the Hodrick-Prescott Filter (1997), originally proposed by Leser (1961). It builds on an approach to seasonal adjustment suggested by Leser (1963) and Schlicht (1981, 1984). A moments estimator for the smoothing parameter is proposed that is asymptotically equivalent to the maximum-likelihood estimator, has a straightforward intuitive interpretation and is more appropriate for short series than the maximum-likelihood estimator. The method is illustrated by an application and several simulations.

Suggested Citation

  • Schlicht, Ekkehart, 2004. "Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter," Discussion Papers in Economics 304, University of Munich, Department of Economics.
    • Handle: RePEc:lmu:muenec:304
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    References listed on IDEAS

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    1. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    2. Schlicht, Ekkehart, 1982. "Seasonal Adjustment in a Stochastic Model," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 38058, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    3. Schlicht, Ekkehart & Pauly, Ralf, 1982. "Descriptive Seasonal Adjustment by Minimizing Perturbations," Darmstadt Discussion Papers in Economics 16, Darmstadt University of Technology, Department of Law and Economics.
    4. Schlicht, Ekkehart, . "Isolation and Aggregation in Economics," Monographs in Economics, University of Munich, Department of Economics, number 3, November.
    5. Schlicht, Ekkehart & Ludsteck, Johannes, 2006. "Variance Estimation in a Random Coefficients Model," Discussion Papers in Economics 904, University of Munich, Department of Economics.
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    Cited by:

    1. Dermoune Azzouz & Djehiche Boualem & Rahmania Nadji, 2009. "Multivariate Extension of the Hodrick-Prescott Filter-Optimality and Characterization," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-35, May.
    2. Blöchl, Andreas, 2014. "Penalized Splines as Frequency Selective Filters - Reducing the Excess Variability at the Margins," Discussion Papers in Economics 20687, University of Munich, Department of Economics.
    3. Dimitrios D. Thomakos, 2008. "Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration," Working Paper series 14_08, Rimini Centre for Economic Analysis.
    4. Baxa, Jaromír & Horváth, Roman & Vašíček, Bořek, 2014. "How Does Monetary Policy Change? Evidence On Inflation-Targeting Countries," Macroeconomic Dynamics, Cambridge University Press, vol. 18(3), pages 593-630, April.
    5. Blöchl, Andreas, 2014. "Trend Estimation with Penalized Splines as Mixed Models for Series with Structural Breaks," Discussion Papers in Economics 18446, University of Munich, Department of Economics.
    6. Baxa, Jaromír & Horváth, Roman & Vašíček, Bořek, 2013. "Time-varying monetary-policy rules and financial stress: Does financial instability matter for monetary policy?," Journal of Financial Stability, Elsevier, vol. 9(1), pages 117-138.
    7. Dermoune, Azzouz & Rahmania, Nadji & Wei, Tianwen, 2012. "General linear mixed model and signal extraction problem with constraint," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 311-321.
    8. David E. Giles, 2013. "Constructing confidence bands for the Hodrick--Prescott filter," Applied Economics Letters, Taylor & Francis Journals, vol. 20(5), pages 480-484, March.
    9. Mr. Francis Vitek, 2014. "Policy and Spillover Analysis in the World Economy: A Panel Dynamic Stochastic General Equilibrium Approach," IMF Working Papers 2014/200, International Monetary Fund.
    10. David E. Giles & Chad N. Stroomer, 2004. "Identifying the Cycle of a Macroeconomic Time-Series Using Fuzzy Filtering," Econometrics Working Papers 0406, Department of Economics, University of Victoria.
    11. knani, ramzi & fredj, ali, 2010. "Mondialisation et fluctuations des cycles économiques [globalisation and business cycle fluctuation]," MPRA Paper 22755, University Library of Munich, Germany.
    12. Itir Ozer & Ibrahim Ozkan, 2008. "Practical Insights From Oca Variable Combinations," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 53(176), pages 38-60, January -.
    13. Bloechl, Andreas, 2014. "Reducing the Excess Variability of the Hodrick-Prescott Filter by Flexible Penalization," Discussion Papers in Economics 17940, University of Munich, Department of Economics.
    14. Metka Stare & Andreja Jaklič, 2011. "Towards Explaining Growth of Private and Public services in the Emerging Market Economies," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 13(30), pages 581-598, June.
    15. Bloechl, Andreas, 2014. "Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter," Discussion Papers in Economics 21406, University of Munich, Department of Economics.
    16. Partouche, H., 2007. "Time-Varying Coefficients in a GMM Framework: Estimation of a Forward Looking Taylor Rule for the Federal Reserve," Working papers 177, Banque de France.
    17. Miroslav Plašil, 2011. "Potenciální produkt, mezera výstupu a míra nejistoty spojená s jejich určením při použití Hodrick-Prescottova filtru [Potential Product, Output Gap and Uncertainty Rate Associated with Their Determ," Politická ekonomie, Prague University of Economics and Business, vol. 2011(4), pages 490-507.
    18. Göran Kauermann & Timo Teuber & Peter Flaschel, 2012. "Exploring US Business Cycles with Bivariate Loops Using Penalized Spline Regression," Computational Economics, Springer;Society for Computational Economics, vol. 39(4), pages 409-427, April.
    19. Itir Ozer & Ibrahim Ozkan, 2007. "Optimum filtering for optimum currency areas criteria," Economics Bulletin, AccessEcon, vol. 6(44), pages 1-18.
    20. Edit V. Velenyi & Marc F. Smitz, 2014. "Cyclical Patterns in Government Health Expenditures Between 1995 and 2010," Health, Nutrition and Population (HNP) Discussion Paper Series 87885, The World Bank.
    21. Posch, Peter N., 2011. "Time to change. Rating changes and policy implications," Journal of Economic Behavior & Organization, Elsevier, vol. 80(3), pages 641-656.

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    More about this item

    Keywords

    Hodrick-Prescott filter; Kalman filter; Kalman-Bucy; Whittaker-Henderson graduation; spline; state-space models; random walk; time-varying coefficients; adaptive estimation; time-series; seasonal adjustment; trend;
    All these keywords.

    JEL classification:

    • 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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