Bloechl, Andreas (2014): Penalized Splines, Mixed Models and the WienerKolmogorov Filter. Discussion Papers in Economics 201444 

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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 HodrickPrescott 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 ARIMAprocesses, 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 WienerKolmogorov filter for a second fold integrated random walk as the trend and a stationary ARMAprocess as the cyclical component.
Item Type:  Paper (Discussion Paper) 

Keywords:  HodrickPrescott filter, mixed models, penalized splines, trend estimation, WienerKolmogorov filter 
Faculties:  Economics > Munich Discussion Papers in Economics 
Subjects:  300 Social sciences > 330 Economics 
JEL Classification:  C220, C520 
URN:  urn:nbn:de:bvb:19epub214069 
Language:  English 
ID Code:  21406 
Deposited On:  08. Sep 2014 08:23 
Last Modified:  30. Apr 2016 17:02 
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