Smoothing methods for short-term trend analysis: cubic splines and Henderson filters

Abstract

This study compares the smoothing properties of cubic splines functions with a very well known short-term trend estimator, the 13-term Henderson filter, and a new procedure developed by Dagum (1996) for the analysis of current economic conditions. The cubic smoothing spline (CSS) trend-cycles are estimated in two ways, namely, (I) using the smoothing parameter obtained with the generalized cross validation criterion and (II) imposing a fixed value found to fit well streches of volatile data present in the series. The comparison, done with a sample of Italian and Canadian series, is based on the number of unwanted ripples and time lag to detect a true turning point. The results are illustrated with four typical cases.