Band Spectral Estimation for Signal Extraction

Abstract

The paper evaluates the potential of band spectral estimation for extracting signals in economic time series. Two situations are considered. The first deals with trend extraction when the original data have been permanently altered by routine operations, such as prefiltering, temporal aggregation and disaggregation, and seasonal adjustment, which modify the high frequencies properties of economic time series. The second is when the measurement model is only partially specified, in that it aims at fitting the series in a particular frequency range, e.g. at interpreting the long run behaviour. These issues are illustrated with reference to a simple structural model, namely the random walk plus noise model.

Stochastic processes of limited frequency and the effects of oversampling

“…An alternative approach to improving the performance of an AR model relies upon a weighted Whittle estimator. This approach had been pursued by various authors including, notably, Haywood and Tunnicliffe -Wilson, (1997) and Proietti (2008). However, it is a delicate matter to find a weighting scheme that will allow one to navigate between the opposing hazards that are represented by the two experiments of the previous section.…”