Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter

Bloechl, Andreas (2014): Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter. Münchener Wirtschaftswissenschaftliche Beiträge (VWL) 2014-44

Abstract

Penalized splines are widespread tools for the estimation of trend and cycle, since they allow a data driven estimation of the penalization parameter by the incorporation into a linear mixed model. Based on the equivalence of penalized splines and the Hodrick-Prescott filter, this paper connects the mixed model framework of penalized splines to the Wiener- Kolmogorov filter. In the case that trend and cycle are described by ARIMA-processes, this filter yields the mean squarred error minimizing estimations of both components. It is shown that for certain settings of the parameters, a penalized spline within the mixed model framework is equal to the Wiener-Kolmogorov filter for a second fold integrated random walk as the trend and a stationary ARMA-process as the cyclical component.

• Dokumententyp: Paper
• Keywords: Hodrick-Prescott filter, mixed models, penalized splines, trend estimation, Wiener-Kolmogorov filter
• Fakultät: Volkswirtschaft > Munich Discussion Papers in Economics
• Themengebiete: 300 Sozialwissenschaften > 330 Wirtschaft
• JEL Classification: C220, C520
• Sprache: Englisch

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