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Title: From detection to forecast of the trend-cycle component in the frequency domain Authors:  Consuelo Nava - University of Aosta Valley (Italy) [presenting]
Maria Grazia Zoia - Catholic University of the Sacred Heart - Milan (Italy)
Abstract: The frequency domain representation of a stochastic process clears the way to a filter-based approach to estimate and predict the trend-cycle component (TCC) of an economic time series. A novel methodology which hinges on a truncated ideal-low pass filter together with a stylized power spectrum (SPS) analyze, is introduced to forecast the TCC. The filter is obtained as a finite approximation of a double infinite Toepliz matrix with sinc functions as entries, to approximate the transfer function of the intended ideal filter. The SPS analyzer is meant to properly locate the cut-off frequency of the filter which must tally with the upper limit frequency of the bandwidth of the TCC. The latter depends on cycle features like evolutiveness, which may yield to a broadening of the original pertinent frequency band. The SPS analyzer, which splits the (average) power of a series throughout the frequency axis, allows to determine the contribution to the power (variability) of the TCC. It is shown how values of the TCC can be duly estimated and predicted by virtue of the almost idempotency of the selected filter and its characteristics. Under suitable assumptions on the erratic component of the series, confidence bounds for the TCC can be estimated in and out of the sample. An application to economic data shows the excellent performance of this approach, whose outcome compares favorably with those of other extant procedures.