Trend Estimation with Penalized Splines as Mixed Models for Series with Structural Breaks

On purpose to extract trend and cycle from a time series many
competing techniques have been developed. The probably most
prevalent is the Hodrick Prescott filter. However this filter
suffers from diverse shortcomings, especially the subjective choice
of its penalization parameter. To this point penalized splines
within a mixed model framework offer the advantage of a data driven
derivation of the penalization parameter. Nevertheless the
Hodrick-Prescott filter as well as penalized splines fail to
estimate trend and cycle when one deals with times series that
contain structural breaks. This paper extends the technique of
splines within a mixed model framework to account for break points
in the data. It explains how penalized splines as mixed models can
be used to avoid distortions caused by breaks and finally provides
an empirical application to German data which exhibit structural
breaks due to the reunification in 1990.