Blöchl, Andreas (April 2014): Penalized Splines as Frequency Selective Filters - Reducing the Excess Variability at the Margins. Münchener Wirtschaftswissenschaftliche Beiträge (VWL) 2014-3 |

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### Abstract

Penalized splines have become a popular tool to model the trend component in economic time series. The outcome of the spline predominantly depends on the choice of a penalization parameter that controls the smoothness of the trend. This paper derives the penalization of splines by frequency domain aspects and points out their link to rational square wave filters. As a novel contribution this paper focuses on the so called excess variability at the margins that describes the undesired increasing variability of the trend estimation to the ends of the series. It will be shown that the too high volatility at the margins can be reduced considerably by a time varying penalization, which yields more reliable estimations for the most recent periods.

Dokumententyp: | Paper (Discussion Paper) |
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Keywords: | excess variability, penalized splines, spectral analysis, time varying penalization, trends |

Fakultät: | Volkswirtschaft
Volkswirtschaft > Munich Discussion Papers in Economics |

Themengebiete: | 300 Sozialwissenschaften > 330 Wirtschaft |

URN: | urn:nbn:de:bvb:19-epub-20687-4 |

Sprache: | Englisch |

ID: | 20687 |

Veröffentlicht am: | 24. Apr. 2014 14:58 |

Letzte Änderungen: | 30. Apr. 2016 09:47 |

Literaturliste: | Altman, N. S. (1990): "Kernel smoothing of data with correlated errors," Journal of the American Statistical Association 85, 749-759. 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. Bell, W. (1984): "Signal extraction for nonstationary time series," Annals of Statistics, 12, 646-664. Blöchl, A. (2014): "Reducing the Excess Variability of the Hodrick-Prescott Filter by Flexible Penalization," Munich Discussion Paper No. 2014-1. Brumback, B. A., Ruppert, D., Wand, M. P. (1999): Comment on "Variable selection and function estimation in additive nonparametric regression using a data-based prior," Journal of the American Statistical Association, 94, 794-797. Burns, A. M., Mitchell, W. C. (1946): "Measuring Business Cycles," New York: National Bureau of Economic Research. Crainiceanu, C., Ruppert, D., Carroll, R. (2005): "Spatially adaptive Bayesian Psplines with heteroscedastic errors," working paper. Dagum, E. B., Giannerini, S. (2006): "A critical investigation on detrending procedures for nonlinear processes," Journal of Macroeconomics, 28 (1), 175-191. Danthine, J., Girardin, M. (1989): "Business Cycles in Switzerland. A Comparative Study," European Economic Review, 33(1), 31-50. Diggle, P. J., Hutchinson, M. F. (1989): "On spline smoothing with autocorrelated errors," Australian Journal of Statistics 31, 166-182. Eilers, P., Marx, B. (1996): "Flexible smoothing with B-splines and penalties," Statistical Science, 11, 89-121. Fahrmeir, L., Kneib, T., Lang, S. (2009): "Regression-Modelle, Methoden und Anwendungen," Springer Verlag, Berlin Heidelberg. Flaig, G. (2012): "Why we should use high values for the smoothing parameter of the Hodrick-Prescott filter," CESifo Working Paper Series No. 3816. Granger, C. W., Hatanaka, M. (1964): "Spectral Analysis of Economic Time Series," Princeton Universtity Press, Princeton/New Jersey. Hamilton, J. D. (1994): "Time Series Analysis," Princeton University Press. Princeton/New Jersey. Hart, J. D. (1991): "Kernel regression estimation with time series errors," Journal of the Royal Statistical Society B 53, 173-187. 6 References 18 Harvey, A., C. (1989): "Forecasting, Structural Time Series Models and the Kallman Filter," Cambridge University Press. Harvey, A. C. (1993): "Time Series Models," Harvester Wheatsheaf, Hertfordshire. Hastie, T., Tibshirani, R. (1990): "Generalized Additive Models," London: Chapman and Hall. Hodrick, R., Prescott, E. (1997): "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking 29, 1-16. Kaiser, R., Maravall, A. (2001): "Measuring Business Cycles in Economic Time Series," Springer Verlag. Kauermann, G., Krivobokova, T., Semmler, W. (2011): "Filtering Time Series with Penalized Splines," Studies in Nonlinear Dynamics and Econometrics 15(2), Article 2. Kohn, R., Ansley, C., Wong, C. (1992): "Nonparametric spline regression with autoregressive moving average errors," Biometrika, 79, 335-346. Krivobokova, T., Kauermann, G. (2007): "A note on penalized spline smoothing with correlated errors," Journal of the American Statistical Association, 102, 1328-1337. 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. Oppenheim, A. V., Schafer, R. W. (1989): "Discrete-Time Signal Processing," Prentice-Hall, Englewood Cliffs, New Jersey. Opsomer, J., Wang, Y., Yang, Y. (2001): "Nonparametric regression with correlated errors," Statistical Science, 16, 134-153. Paige, R. L. (2010): "The Hodrick-Prescott filter: A special case of penalized spline smoothing," Electronic Journal of Statistics, 4, 856-874. Pollock, D. S. G. (2000): "Trend estimation and de-trending via rational square-wave filters," Journal of Econometrics 99, 317-334. Pollock, D. S. G. (2003): "Improved frequency selective filters," Computational Statistics & Data Analysis 42, 279-297. Pollock, D. S. G. (2009): "Improved frequency selective filters," Computational Statistics & Data Analysis 42, 279-297. 6 References 19 Proietti, T. (2005): "Forecasting and signal extraction with misspecified models," Journal of Forecasting, 24, 539-556. Proietti, T. (2007): "Signal Extraction and Filtering by Linear Semiparametric Methods," Computational Statistics and Data Analysis 52, 935-958. 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. Ruppert, D. (2002): "Selecting the number of knots for penalized splines," Journal of Computational and Graphical Statistics, 11, 735-757. Ruppert, D., Wand, M., Carroll, R. (2003): "Semiparametric Regression," Cambridge University Press. 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. 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. Wang, Y. (1998): "Mixed effects smoothing spline analysis of variance," Journal of the Royal Statistical Society, Series B, 60, 159-174. Whittle, P. (1983): "Prediction and Regulation," Blackwell. |