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 Hodrick-Prescott filter is the probably most popular tool for trend estimation in economics. Compared to other frequently used methods like the Baxter-King filter it allows to estimate the trend for the most recent periods of a time series. However, the Hodrick- Prescott filter suffers from...

Trend extraction from time series is often performed by using the filter proposed by Leser (1961), also known as the Hodrick-Prescott filter. A practical problem arises, however, when some data points are missing. This note proposes a method for coping with this problem.

This note gives a fairly complete statistical description of the Hodrick-Prescott Filter (1997), originally proposed by Leser (1961). It builds on an approach to seasonal adjustment suggested by Leser (1963) and Schlicht (1981, 1984). A moments estimator for the smoothing parameter is proposed...

Trend extraction from time series is often performed by using the filter proposed by Leser (1961), also known as the Hodrick-Prescott filter. A practical problem arises, however, when the time series contains structural breaks (such as produced by German unification for German time series, for...

Trend extraction from time series is often performed by using the filter proposed by Leser (1961), also known as the Hodrick-Prescott filter. Practical problems arise, however, if the time series contains structural breaks (as produced by German unification for German time series, for instance),...