Periodically Correlated Time Series

A coherent presentation of material scattered in journal papers is given. The relationship between periodic models and multiple ARMA models is discussed and employed to make the investigation of these two classes theoretically equivalent. This book discusses notation and representation issues for periodic autoregressive models for univariate periodic time series. In addition, a new representation, the multi-companion (MC) presentation is proposed. This book also reviews the application of the maximum entropy principle to time series and obtain some new results. The main contribution is that it solves the autocovariance extension problem in a far more general setting than previously known. The study of entropy was motivated by periodic correlation but the main results on this topic are more general. A formula for the entropy of a periodically correlated process is given and seems to be new. Finally, the book proposes a method for generation of periodically correlated models with given spectral properties which has no analogue in the literature.