Further Developments on the Henderson Trend-Cycle Filter

The linear filter developed by Henderson is the most widely applied to estimate the trend-cycle component in seasonal adjustment software such as the US Bureau of Census II-X11 and its variants, the X11/X12ARIMA. Major studies have been done on trend-cycle estimation during the last 20 years by making changes to the Henderson filters. The emphasis has been on determining the direction of the short-term trend for an early detection of a true turning point. This chapter introduces in detail three major contributions: (1) a nonlinear trend-cycle estimator also known as Nonlinear Dagum Filter (NLDF), (2) a Cascade Linear Filter (CLF) that closely approximates the NLDF, and (3) an approximation to the Henderson filter via the Reproducing Kernel Hilbert Space (RKHS) methodology.