La stima del ciclo-trend col metodo delle funzioni sferoidali prolate

Abstract

This paper develops a new method of trend-cycle estimation. According to the authors' frequency-domain characterization of latent components in economic time series, trend-cycle turns out to be a band-limited signal, located within the low-middle frequency range. Hence, the aforesaid component can be represented, resting on Landau and Pollak's smart theorems, in terms of a properly chosen set of prolate spheroidal functions and, what is more, it can be detected by projecting the observed series onto the subspace of band-limited sequences spanned by such functions. The paper plainly sets forth the theoretical frame and the technicalities of the suggested novel method of trend-cycle estimation and discusses a few of its operational aspects.