|Bloechl, Andreas (2014): Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter. Discussion Papers in Economics 2014-44|
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.
|Item Type:||Paper (Discussion Paper)|
|Keywords:||Hodrick-Prescott filter, mixed models, penalized splines, trend estimation, Wiener-Kolmogorov filter|
|Faculties:||Economics > Munich Discussion Papers in Economics|
|Subjects:||300 Social sciences > 330 Economics|
|JEL Classification:||C220, C520|
|Deposited On:||08. Sep 2014 08:23|
|Last Modified:||30. Apr 2016 17:02|
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