Econometric Filters

A variety of filters that are commonly employed by econometricians are analysed with a view to determining their effectiveness in extracting well-defined components of economic data sequences. These components can be defined in terms of their spectral structures—i.e. their frequency content—and it is argued that the process of econometric signal extraction should be guided by a careful appraisal of the periodogram of the detrended data sequence. A preliminary estimate of the trend can often be obtained by fitting a polynomial function to the data. This can provide a firm benchmark against which the deviations of the business cycle and the fluctuations of seasonal activities can be measured. The trend-cycle component may be estimated by adding the business cycle estimate to the trend function. In cases where there are evident structural breaks in the data, other means are suggested for estimating the underlying trajectory of the data. Whereas it is true that many annual and quarterly economic data sequences are amenable to relatively unsophisticated filtering techniques, it is often the case that monthly data that exhibit strong seasonal fluctuations require a far more delicate approach. In such cases, it may be appropriate to use filters that work directly in the frequency domain by selecting or modifying the spectral ordinates of a Fourier decomposition of data that have been subject to a preliminary detrending