Penalized splines have become a popular tool to model the trend component in economic time series. The outcome of the spline predominantly depends on the choice of a penalization parameter that controls the smoothness of the trend. This paper derives the penalization of splines by frequency...

In this paper we revisit the methodological aspects of the issue of spurious cycles: using the well-established clinometric data, we apply an empirical strategy to identify spurious periodicities and cross-validate the results. The analysis of cyclical fluctuations involves numerous challenges,...