A new smoothing technique for univariate time series: the endpoint problem

Many filters have been developed to estimate trend-cycle component of time series. Among these tools, moving averages remain the most efficient. In particular, while the symmetric Henderson smoother is applied for trend-cycle estimation in software programs such as X11, for the most recent observations, it may be necessary to use asymmetric filters. In this regard, we propose a new smoothing method, based on the Epanechnikov kernel, to treat endpoints. We then compare this method with the Henderson filter on a data sample.