Spectral expressions of information measures of Gaussian time series and their relation to AIC and CAT

Interrelations among the spectral expressions of the information measures of Kullback-Leibler (1959) and Renyi (1961) for discrimination between two stationary Gaussian time series are discussed. The spectral expression of Fisher´s information rate matrix is also treated, as well as two intuitively acceptable discrimination functions. It is shown that all of them are equivalent except for scalar multiplication and are expressed by Fisher´s information rate matrix in the sense of their second-order Taylor series approximation. Finally, a relation between two criteria for order determination of models for time series data, namely, H. Akaike´s (1974) information criterion (AIC) and the criterion of autoregressive transfer functions (CAT), is discussed in connection with these spectral expressions