Blöchl, Andreas (February 2014): Trend Estimation with Penalized Splines as Mixed Models for Series with Structural Breaks. Discussion Papers in Economics 20142 

444kB 
Abstract
On purpose to extract trend and cycle from a time series many competing techniques have been developed. The probably most prevalent is the Hodrick Prescott filter. However this filter suffers from diverse shortcomings, especially the subjective choice of its penalization parameter. To this point penalized splines within a mixed model framework offer the advantage of a data driven derivation of the penalization parameter. Nevertheless the HodrickPrescott filter as well as penalized splines fail to estimate trend and cycle when one deals with times series that contain structural breaks. This paper extends the technique of splines within a mixed model framework to account for break points in the data. It explains how penalized splines as mixed models can be used to avoid distortions caused by breaks and finally provides an empirical application to German data which exhibit structural breaks due to the reunification in 1990.
Item Type:  Paper (Discussion Paper) 

Keywords:  penalized splines, mixed models, structural breaks, trends, flexible penalization 
Faculties:  Economics Economics > Munich Discussion Papers in Economics 
Subjects:  300 Social sciences > 330 Economics 
JEL Classification:  C220, C520 
URN:  urn:nbn:de:bvb:19epub184462 
Language:  English 
ID Code:  18446 
Deposited On:  10. Mar 2014 07:57 
Last Modified:  30. Apr 2016 05:54 
References:  Bell, W. (1984): "Signal Extraction for nonstationary time series," Annals of Statistics, 12, 646664. Brumback, B. A., Ruppert, D., Wand, M. P. (1999): Comment on "Variable selection and function estimation in additive nonparametric regression using a databased prior," Journal of the American Statistical Association, 94, 794797. Claeskens, G., Krivobokova, T., Opsomer, J. (2009): "Asymptotic properties of penalized spline estimators," Biometrika, 96, 529544. Crainiceanu, C., Ruppert, D., Carroll, R., (2004): "Spatially adaptive Bayesian Psplines with heteroscedastic errors." Johns Hopkins University Dept. of Biostatistics Working Paper Series No. 1061, Berkeley Electronic Press. Danthine, J., Girardin, M., (1989); "Business Cycles in Switzerland. A Comparative Study," European Economic Review, 33(1), S. 3150. Fahrmeir, L., Kneib, T., Lang, S., (2009): "Regression  Modelle, Methoden und Anwendungen," Springer Verlag, Berlin Heidelberg. Hayes, K., Haslett, J. (1999): "Simplifying general least squares," American Statistician, 53, 376381. Henderson, R. (1924): "On a new method of graduation," Transactions of the Actuarial Society of America, 25, 2940. Hodrick, R., J., Prescott, E., C., (1997); "PostWar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, 29, 116. Krivobokova, T., Kauermann, G., (2007): "A note on penalized spline smoothing with correlated errors," Journal of the American Statistical Association, 102, 13281337. Kauermann, G., Krivobokova, T., Semmler, W., (2011): "Filtering Time Series with Penalized Splines," Studies in Nonlinear Dynamics & Econometrics, 15(2), Article 2. Kauermann, G., Opsomer, J., (2011): :"Datadriven selection of the spline dimension in penalized spline regression," Biometrika, 98(1), 225230. Leser, C., E., V., (1961): "A simple method of trend construction," Journal of the Royal Statistical Society. Series B (Methodological), 23, 91107. McCulloch, C. E., Searle, S. R. (2001): "Generalized, Linear, and Mixed Models," New York: Wiley. 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 illposed inverse problems (c/r:P519 527)," Statistical Science, 1, 502518. Paige, R. L. (2010): "The HodrickPrescott filter: A special case of penalized spline smoothing," Electronic Journal of Statistics, 4, 856874. Pinheiro, J. C., Bates, D. M. (2000): "MixedEffects Models in S and SPLUS," New York: SpringerVerlag. Pollock D. S. G. (2009): "Investigating economic trends and cycles," Boumans, M. (Ed.), Palgrave Handbook of Econometrics, Volume 2: Applied Econometrics, Palgrave Macmillan, 243307. Proietti, T., Luati, A. (2007): "Least Squares Regression: Graduation and Filters," Boumans, M. (Ed.), Measurement in Economics: A Handbook, ch. 16, Academic Press. Ravn, M. O., Uhlig, H., (2002): "On adjusting the HodrickPrescott filter for the frequency of observations," The Review of Economics and Statistics, 84, 371380. Razzak, W., Richard, D., (1995): "Estimates of New Zealand’s Output Gap using the Hodrick Prescott filter with an nonconstant Smoothing Parameter," Reserve Bank of New Zealand, Discussion Paper G95/8. Robinson, G. K. (1991): "That BLUP s a good thing: The estimation of random effects," Statistical Science, 6, 1551. Ruppert, D. (2002): "Selecting the number of knots for penalized splines," Journal of Computational and Graphical Statistics, 11, 735757. Ruppert, R.,Wand, M., Carroll, R., (2003): "Semiparametric Regression," Cambridge University Press. Schlicht, E. (2005): "Estimating the Smoothing Parameter in the socalled HodrickPrescott Filter," Journal of the Japanese Statistical Society, Vol. 35 No. 1, 99119. Schlicht, E. (2008): "Trend Extraction from Time Series with Structural Breaks and Missing Observations," Journal of the Japanese Statistical Society, Vol. 38 No. 2, 205292. Searle, S. R., Casella, G., McCulloch, C. E. (1992): "Variance Components," New York: Wiley. Stamfort, S., (2005): "Berechnung trendbereinigter Indikatoren für Deutschland mit Hilfe von Filterverfahren," Deutsche Bundesbank, Discussion Paper Nr. 19. Vonesh, E. F., Chinchilli, V. M. (1997): "Linear and Nonlinear Models for the Analysis of Repeated Measures," New York: Marcel Dekker. Whittaker, E.,T., (1923): "On a new method of graduation," Proceedings of the Edinburgh Mathematical Society, 41, 6375. Whittle, P. (1983): "Prediction and Regulation," Blackwell. 