Parameter time-frequency representations

The definition and representation of time varying spectra are discussed. The definitions of Priestley (1965), Tjostheim (1976) and Grenier (1984) are examined. It is shown that the adjusted average autoregressive models may be globally unstable in spite of the stability of their limit models. The analysis finds that the Tjostheim definition and the observable state definition are equivalent in the sense that the first respects the signal variance and the second the instantaneous local conditions.