Identification and estimation of economic time series components: an integrated approach resting on both time and frequency domain arguments

Abstract

This paper deals with the issues of modeling economic time series and identifying the underlying latent components from both a time and a frequency domain standpoint. Thus, the crucial problem of component estimation is tackled by filter theory arguments. On the one hand, the band-limited frequency property of the trend-cycle, which ensues from the time domain component characterisation, leads to look at the relevant estimation issue as a low-pass filtering problem. On the other hand, the interpretation of the evolutive mechanism of seasonality as an amplitude modulation process, due to longer period components, suggests the adoption of a detection algorithm for estimation purposes. Moreover, the genuine seasonal pattern is obtained by passing the unmodulated seasonal component through a properly designed wave selector filter and the associated nuisance component enables to estimate the error term as well. Eventually the whole procedure for estimating the latent components of time series is put into an impressive flow chart.