Local Polynomial Regression in Real Time

The concern of the paper is real time estimation of the underlying trend in a time series by means of filters that arise from fitting a local polynomial of a given degree with a constant bandwidth. After reviewing the constructive principles presiding the derivation of the two-sided symmetric local polynomial filters, we provide a thorough assessment of the properties of the asymmetric filters automatically adapted at the boundary, which result from fitting a local polynomial with a fixed bandwidth to the observations available at the current time. We propose an alternative class of fixed bandwidth asymmetric filters that result from minimising the mean square revision error subject to polynomial reproduction constraints. This class generalises the well known Musgrave's asymmetric approximation of the Henderson filters.