Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter

Andreas Bloechl

Discussion Papers in Economics from University of Munich, Department of Economics

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.

Keywords: Hodrick-Prescott filter; mixed models; penalized splines; trend estimation; Wiener-Kolmogorov filter (search for similar items in EconPapers)
JEL-codes: C22 C52 (search for similar items in EconPapers)
Date: 2014
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-for and nep-ger
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Persistent link: https://EconPapers.repec.org/RePEc:lmu:muenec:21406

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