Generalized Linear Spectral Models for Locally Stationary Processes

A class of parametric models for locally stationary processes is introduced. The class depends on a power parameter that applies to the time-varying spectrum so that it can be locally represented by a (finite 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 static parameters. Frequency domain estimation is based on the generalized Whittle likelihood and the pre-periodogram, while model selection is performed through information criteria. Change points are identified 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.