IDEOLOG: A Program for Filtering Econometric Data - A Synopsis of Alternative Methods

An account is given of various filtering procedures that have been implemented in a computer program, which can be used in analysing econometric time series. The program provides some new filtering procedures that operate primarily in the frequency domain. Their advantage is that they are able to achieve clear separations of components of the data that reside in adjacent frequency bands in a way that the conventional time-domain methods cannot. Several procedures that operate exclusively within the time domain have also been implemented in the program. Amongst these are the bandpass filters of Baxter and King and of Christiano and Fitzgerald, which have been used in estimating business cycles. The Henderson filter, the Butterworth filter and the Leser or Hodrick–Prescott filter are also implemented. These are also described in this paper. Econometric filtering procedures must be able to cope with the trends that are typical of economic time series. If a trended data sequence has been reduced to stationarity by differencing prior to its filtering, then the filtered sequence will need to be re-inflated. This can be achieved within the time domain via the summation operator, which is the inverse of the difference operator. The effects of the differencing can also be reversed within the frequency domain by recourse to the frequency-response function of the summation operator.