Spectral Models for Locally Stationary Time Series

A flexible class of parametric models for locally stationary processes is introduced. The class depends on a power parameter that applies to the spectrum so that it can be locally represented by a finite, and low dimensional, Fourier polynomial. The coefficients of the polynomial have an interpretation as time varying autocovariances, whose dynamics are determined by a linear combination of smooth transition functions, depending on some. Frequency domain estimation is based on the generalised Whittle likelihood and the preperiodogram while model selection is performed through information criteria. Changepoints are obtained via a sequence of score tests. Consistency and asymptotic normality are proved for the parametric estimators considered in the paper, under weak assumptions on the time varying parameters and by assuming independent errors.

Joint with: Tommaso Proietti, Stefano Grassi, University of Rome Tor Vergata.