Generalised autocovariances and spectral estimators

A class of models for the time-varying spectrum of a locally stationary process is introduced. The models are specified in the frequency domain and the class depends on a power parameter that applies to the spectrum so that it can be locally represented by a finite Fourier polynomial. The coefficients of the polynomial are dynamic generalised cepstral coefficients that have an interpretation as generalised autocovariances. The dynamics of the generalised cepstral coefficients are determined according to a linear combination of logistic transition functions of the time index. Estimation is carried out in the frequency domain based on the generalised Whittle likelihood.