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

This chapter presents some novel information theoretic results for the analysis of stationary time series in the frequency domain. In particular, the spectral distribution that corresponds to the most uncertain or unpredictable time series with some values of the autocovariance function fixed, is the generalized von Mises spectral distribution. It is thus a maximum entropy spectral distribution and the corresponding stationary time series is called the generalized von Mises time series. The generalized von Mises distribution is used in directional statistics for modelling planar directions that follow a multimodal distribution. Furthermore, the Gaussian-generalized von Mises times series is presented as the stationary time series that maximizes entropies in frequency and time domains, respectively referred to as spectral and temporal entropies. Parameter estimation and some computational aspects with this time series are briefly analyzed.