  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.
