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Gaussian and Non-Gaussian Linear Time Series and Random Fields
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The book is concerned with linear time series and random fields in both the Gaussian and especially the non-Gaussian context. The principal focus is on autoregressive moving average models and analogous random fields. Probabilistic and statistical questions are both discussed. The Gaussian models are contrasted with noncausal or noninvertible (nonminimum phase) non-Gaussian models which can have a much richer structure than Gaussian models. The book deals with problems of prediction (which can have a nonlinear character) and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. The book is intended as a text for graduate students in statistics, mathematics, engineering, the natural sciences and economics. An initial background in probability theory and statistics is suggested. Notes on background, history and open problems are given at the end of the book.
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