Andreas Bloechl: Penalized Splines, Mixed Models and the Wiener-kolmogorov Filter Penalized Splines, Mixed Models and the Wiener-kolmogorov Filter
نویسنده
چکیده
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 WienerKolmogorov 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. JEL-Code: C220, C520
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Andreas Blöchl: Trend Estimation with Penalized Splines as Mixed Models for Series with Structural Breaks
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