Gaussian and Non-Gaussian Linear Time Series and Random Fields

AvMurray Rosenblatt

Inbunden, Engelska, 1999

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Beskrivning

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. Murray Rosenblatt is Professor of Mathematics at the University of California, San Diego. He was a Guggenheim Fellow in 1965 and 1972 and is a member of the National Academy of Sciences, U.S.A.He is the author of Random Processes (1962), Markov Processes: Structure and Asymptotic Behavior (1971), Stationary Sequences and Random Fields (1985), and Stochastic Curve Estimation (1991).

Produktinformation

Utgivningsdatum:1999-12-21
Mått:155 x 235 x 20 mm
Vikt:571 g
Format:Inbunden
Språk:Engelska
Serie:Springer Series in Statistics
Antal sidor:247
Upplaga:2000
Förlag:Springer-Verlag New York Inc.
ISBN:9780387989174

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik

Recensioner i media

From the reviews: SHORT BOOK REVIEWS "...will make this book useful as a reference source to the more theoretical among time series specialists." ZENTRALBLATT MATH "This publication can be recommended to readers familiar with the basic concepts of time series who are interested in estimation problems in nonminimum phase processes."

Innehållsförteckning

1 Reversibility and Identifiability.- 1.1 Linear Sequences and the Gaussian Property.- 1.2 Reversibility.- 1.3 Identifiability.- 1.4 Minimum and Nonminimum Phase Sequences.- 2 Minimum Phase Estimation.- 2.1 The Minimum Phase Case and the Quasi-Gaussian Likelihood.- 2.2 Consistency.- 2.3 The Asymptotic Distribution.- 3 Homogeneous Gaussian Random Fields.- 3.1 Regular and Singular Fields.- 3.2 An Isometry.- 3.3 L-Fields and L-Markov Fields.- 4 Cumulants, Mixing and Estimation for Gaussian Fields.- 4.1 Moments and Cumulants.- 4.2 Higher Order Spectra.- 4.3 Some Simple Inequalities and Strong Mixing.- 4.4 Strong Mixing for Two-Sided Linear Processes.- 4.5 Mixing and a Central Limit Theorem for Random Fields.- 4.6 Estimation for Stationary Random Fields.- 4.7 Cumulants of Finite Fourier Transforms.- 4.8 Appendix: Two Inequalities.- 5 Prediction for Minimum and Nonminimum Phase Models.- 5.1 Introduction.- 5.2 A First Order Autoregressive Model.- 5.3 Nonminimum Phase Autoregressive Models.- 5.4 A Functional Equation.- 5.5 Entropy.- 5.6 Continuous Time Parameter Processes.- 6 The Fluctuation of the Quasi-Gaussian Likelihood.- 6.1 Initial Remarks.- 6.2 Derivation.- 6.3 The Limiting Process.- 7 Random Fields.- 7.1 Introduction.- 7.2 Markov Fields and Chains.- 7.3 Entropy and a Limit Theorem.- 7.4 Some Illustrations.- 8 Estimation for Possibly Nonminimum Phase Schemes.- 8.1 The Likelihood for Possibly Non-Gaussian Autoregressive Schemes.- 8.2 Asymptotic Normality.- 8.3 Preliminary Comments: Approximate Maximum Likelihood Estimates for Non-Gaussian Nonminimum Phase ARMA Sequences.- 8.4 The Likelihood Function.- 8.5 The Covariance Matrix.- 8.6 Solution of the Approximate Likelihood Equations.- 8.7 Cumulants and Estimation for Autoregressive Schemes.- 8.8 Superefficiency.- Bibliographic Notes.- References.- Notation.- Author Index.