A comparison of new developments of the Henderson filters for real time trend-cycle estimation

The Henderson filters (1916) jointly with the Musgrave filters (1964) have been used for trend-cycle estimation in officially published data by statistical agencies around the world. The Henderson filters are symmetric and the Musgrave ones are asymmetric and we shall refer to both as symmetric and asymmetric Henderson filters. These filters have the good property of fast detection of true turning points, but the limitations of large revisions when data are added, and a large amount of unwanted ripples (9 and 10 month cycles) for short filter lengths. The purpose of this paper is to present a brief description of three estimators developed to reduce the Henderson filter limitations. We do so from a theoretical viewpoint by looking at the respective gain and phase shift functions and empirically by application to a sample of economic indicators. We calculate the mean square revision error as new observations are added to the series and the time delay to estimate a turning point that for illustrative purposes we have chosen to be December 2007