Local polynomial trend-cycle predictors in reproducing kernel Hilbert spaces for current economic analysis

The local polynomial regression predictors developed by Henderson (1916) and LOESS due to Cleveland (1979) are widely applied to estimate the short-term trend of socioeconomic indicators. The main purpose of this study is to introduce a RKHS representation of the Henderson and LOESS smoothers with particular emphasis on the asymmetric ones applied to most recent observations. The asymmetric filters can be derived coherently with the corresponding symmetric weights or from a lower or higher order kernel within a hierarchy, if more appropriate. In the particular case of the currently applied asymmetric Henderson and LOESS filters, those obtained by means of the RKHS are shown to have superior properties relative to the classical ones from the view point of signal passing, noise suppression and revisions. We compare the performance of the kernel representations relative to the classical filters using real life series.