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Titlebook: Gaussian and Non-Gaussian Linear Time Series and Random Fields; Murray Rosenblatt Book 2000 Springer Science+Business Media New York 2000

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书目名称Gaussian and Non-Gaussian Linear Time Series and Random Fields
编辑Murray Rosenblatt
视频video
丛书名称Springer Series in Statistics
图书封面Titlebook: Gaussian and Non-Gaussian Linear Time Series and Random Fields; Murray Rosenblatt Book 2000 Springer Science+Business Media New York 2000
描述Much of this book is concerned with autoregressive and moving av­ erage linear stationary sequences and random fields. These models are part of the classical literature in time series analysis, particularly in the Gaussian case. There is a large literature on probabilistic and statistical aspects of these models-to a great extent in the Gaussian context. In the Gaussian case best predictors are linear and there is an extensive study of the asymptotics of asymptotically optimal esti­ mators. Some discussion of these classical results is given to provide a contrast with what may occur in the non-Gaussian case. There the prediction problem may be nonlinear and problems of estima­ tion can have a certain complexity due to the richer structure that non-Gaussian models may have. Gaussian stationary sequences have a reversible probability struc­ ture, that is, the probability structure with time increasing in the usual manner is the same as that with time reversed. Chapter 1 considers the question of reversibility for linear stationary sequences and gives necessary and sufficient conditions for the reversibility. A neat result of Breidt and Davis on reversibility is presented. A sim­ ple
出版日期Book 2000
关键词Covariance matrix; Gaussian Linear Time Series; Likelihood; Linear Time Series; Probability theory; Time
版次1
doihttps://doi.org/10.1007/978-1-4612-1262-1
isbn_softcover978-1-4612-7067-6
isbn_ebook978-1-4612-1262-1Series ISSN 0172-7397 Series E-ISSN 2197-568X
issn_series 0172-7397
copyrightSpringer Science+Business Media New York 2000
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Gaussian and Non-Gaussian Linear Time Series and Random Fields
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Book 2000e increasing in the usual manner is the same as that with time reversed. Chapter 1 considers the question of reversibility for linear stationary sequences and gives necessary and sufficient conditions for the reversibility. A neat result of Breidt and Davis on reversibility is presented. A sim­ ple
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Bedingte Reflexe, die Lernmatrix,Later on a number of methods will be introduced that are based on moments of cumulants and are used to estimate aspects of the structure of processes of interest. For this reason it seems proper to make some remarks about moments and cumulants and the relationship between them.
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https://doi.org/10.1007/978-3-662-00604-7Assume that . is a stationary ARMA scheine satisfying the system of equations. where the ξ.’s are independent and identically distributed with .ξ. = 0 and .ξ. = σ. > 0. Consider the prediction problem in which one approximates x. by a function of x., s ≤ 0, in mean square as well as one can.
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Reversibility and Identifiability,Let us first consider linear stationary sequences. A sequence of independent, identically distributed real random variables ξ., j = …, -1,0,1,… is given with Eξ. = 0, 0 < .ξ. = σ. < ∞. The process x. is obtained by passing this sequence through a linear filter characterized by the real weights, ., ∑. < ∞,
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