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This chapter presents some novel information theoretic results for theanalysis of stationary time series in the frequency domain. In particular, thespectral distribution that corresponds to the most uncertain or unpredictabletime series with some values of the autocovariance function fixed, is thegeneralized von Mises spectral distribution. It is thus a maximum entropyspectral distribution and the corresponding stationary time series is calledthe generalized von Mises time series. The generalized von Mises distributionis used in directional statistics for modelling planar directions that follow amultimodal distribution. Furthermore, the Gaussian-generalized von Mises timesseries is presented as the stationary time series that maximizes entropies infrequency and time domains, respectively referred to as spectral and temporalentropies. Parameter estimation and some computational aspects with this timeseries are briefly analyzed.

Information theoretic results for stationary time series and the Gaussian-generalized von Mises time series