Reducing the Excess Variability of the Hodrick-Prescott Filter by Flexible Penalization

Bloechl, Andreas (January 2014): Reducing the Excess Variability of the Hodrick-Prescott Filter by Flexible Penalization. Discussion Papers in Economics 2014-1

Abstract

The Hodrick-Prescott filter is the probably most popular tool for trend estimation in economics. Compared to other frequently used methods like the Baxter-King filter it allows to estimate the trend for the most recent periods of a time series. However, the Hodrick- Prescott filter suffers from an increasing excess variability at the margins of the series inducing a too flexible trend function at the margins compared to the middle. This paper will tackle this problem using spectral analysis and a flexible penalization. It will show that the excess variability can be reduced immensely by a flexible penalization, while the gain function for the middle of the time series is used as a measure to determine the degree of the flexible penalization.

• Item Type: Paper
• Keywords: Hodrick-Prescott filter, spectral analysis, trend estimation, gain function, flexible penalization
• Faculties: Economics; Economics > Munich Discussion Papers in Economics
• Subjects: 300 Social sciences > 330 Economics
• JEL Classification: C220, C520
• Language: English

References

Baxter, M., King, R. (1999): "Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series," The Review of Economics and Statistics 81, 575-593.

Bruchez, P. A. (2003): "A Modification of the HP-filter - Aiming at Reducing the End- Point Bias," Swiss Federal Finance Administration, Working Paper.

Colgley, T., Nason, J. (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 19, 253-278.

Crainiceanu, C., Ruppert, D., Carroll, R. (2005): "Spatially adaptive Bayesian P-splines with heteroscedastic errors," Working Paper.

Danthine, J., Girardin, M. (1989): "Business Cycles in Switzerland. A Comparative Study," European Economic Review, 33(1), 31-50.

Flaig, G. (2012): "Why we should use high values for the smoothing parameter of the Hodrick-Prescott filter," CESifo Working Paper Series No. 3816.

Hamilton, J. D. (1994): "Time Series Analysis," Princeton University Press, Princeton/ New Jersey.

Harvey, A. C. (1993): "Time Series Models," Harvester Wheatsheaf, Hertfordshire. Hodrick, R., Prescott, E. (1997): "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking 29, 1-16.

Kauermann, G., Krivobokova, T., Semmler, W. (2011): "Filtering Time Series with Penalized Splines," Studies in Nonlinear Dynamics and Econometrics 15(2), Article 2.

King, R., Rebelo, S. (1993): "Low Frequency filtering and real business cycles," Journal of Economic Dynamics and Control 17, 207-231.

Maravall, A., del Rio, A. (2001): "Time Aggregation and the Hodrick-Prescott-Filter," Banco de Espana Servicio de Estudios, Documento de Trabajo n. 0108.

McCallum, B. T. (2000): "Alternative monetary policy rules: A comparison with historical settings for the United States, the United Kingdom and Japan," Economic Quarterly of the Federal Reserve Bank of Richmond, 86, 49-79.

McElroy, T. (2008): "Matrix Formulas for Nonstationary ARIMA Signal Extraction," Econometric Theory 24, 988-1009.

Mills, T. C. (2003): "Modelling Trends and Cycles in Economic Time Series," Palgrave Macmillan, Houndmills/Basingstoke/Hampshire/New York.

O’Sullivan, F. (1986): "A statistical perspective on ill-posed inverse problems (c/r: P519- 527)," Statistical Science, 1, 502-518.

Proietti, T. (2007): "Signal Extraction and Filtering by Linear Semiparametric Methods," Computational Statistics and Data Analysis 52, 935-958.

Proietti, T., Luati, A. (2007): "Least Squares Regression: Graduation and Filters," Boumans, M. (Ed.), Measurement in Economics: A Handbook, ch. 16, Academic Press.

Razzak, W., Richard, D. (1995): "Estimates of New Zealand’s Output Gap using the Hodrick Prescott filter with an non-constant Smoothing Parameter," Reserve Bank of New Zealand, Discussion Paper G95/8.

Schlicht, E. (2005): "Estimating the Smoothing Parameter in the so-called Hodrick-Prescott Filter," Journal of the Japanese Statistical Society, Vol. 35 No. 1, 99-119.

Stamfort, S. (2005): "Berechnung trendbereinigter Indikatoren für Deutschland mit Hilfe von Filterverfahren," Deutsche Bundesbank, Diskussionspapier Nr. 19.

Tödter, K. H. (2002): "Exponential Smoothing as an Alternative to the Hodrick-Prescott Filter," Contributions to Modern Econometrics-From Data Analysis to Economic Policy. Boston: Kluwer Academic Publishers, S. 223-237.