Econometric methods of signal extraction

The Wiener–Kolmogorov signal extraction filters, which are widely used in econometric analysis, are constructed on the basis of statistical models of the processes generating the data. The models can be heuristic devices that may be specified in whichever ways are appropriate to ensure that the filters have the desired characteristics. The digital Butterworth filters, which are described and illustrated in the paper, are specified in this way. The components of an econometric time series often give rise to spectral structures that fall within well-defined frequency bands that are isolated from each other by spectral dead spaces. For such cases, a Fourier-based method is proposed, which operates in the frequency domain. This new method can be assimilated to a finite-sample Wiener–Kolmogorov framework.