On a family of finite moving-average trend filters for the ends of series

A family of finite end filters is constructed using a minimum revisions criterion and based on a local dynamic model operating within the span of a given finite central filter. These end filters are equivalent to evaluating the central filter with unavailable future observations replaced by constrained optimal linear predictions. Two prediction methods are considered: best linear unbiased prediction and best linear prediction where the bias is time variant. The properties of these end filters are determined. In particular, they are compared to X-11 end filters and to the case where the central filter is evaluated with unavailable future observations predicted by global ARIMA models as in X-11-ARIMA or X-12-ARIMA.