Evaluating reliability of some symmetric and asymmetric univariate filters

Abstract

This paper examines statistical reliability of univariate filters for estimation of trend in leading indicators of cyclical changes. For this purpose, three measures are used: mean square error for quantitative accuracy, minimum revisions with additional data for statistical accuracy and directional accuracy to capture property of signaling cyclical movements. Our focus is on the widely used Hodrick-Prescott and Henderson filters and their generalizations to splines and RKHS(Reproducing Kernel Hilbert Spaces) embedding respectively. Comparison of trend fitted by the filters is illustrated with Indian and US Industrial production data and a simulated data series. We find that although Henderson smoothers based on RKHS preform better than classical filter, they are not better than spline based methods on the selected criterion for Indian macroeconomic time series. Overall findings suggest that in cases when penalized splines converge in quasi real time, they are better than HP filter on the three criterion.