Real time estimation in local polynomial regression, with application to trend-cycle analysis

TL;DR

This paper develops and evaluates asymmetric filters for real-time trend-cycle estimation in local polynomial regression, addressing volatility issues at the data boundary and improving estimation accuracy.

Contribution

It introduces a family of asymmetric filters that minimize revision errors and adapt to unknown signal features, enhancing real-time trend estimation.

Findings

Asymmetric filters reduce volatility in real-time estimates.

The proposed filters outperform traditional methods in empirical examples.

Estimation of signal features improves filter performance.

Abstract

The paper focuses on the adaptation of local polynomial filters at the end of the sample period. We show that for real time estimation of signals (i.e., exactly at the boundary of the time support) we cannot rely on the automatic adaptation of the local polynomial smoothers, since the direct real time filter turns out to be strongly localized, and thereby yields extremely volatile estimates. As an alternative, we evaluate a general family of asymmetric filters that minimizes the mean square revision error subject to polynomial reproduction constraints; in the case of the Henderson filter it nests the well-known Musgrave's surrogate filters. The class of filters depends on unknown features of the series such as the slope and the curvature of the underlying signal, which can be estimated from the data. Several empirical examples illustrate the effectiveness of our proposal.