© 2000

Gaussian and Non-Gaussian Linear Time Series and Random Fields


Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Murray Rosenblatt
    Pages 1-13
  3. Murray Rosenblatt
    Pages 15-26
  4. Murray Rosenblatt
    Pages 27-39
  5. Murray Rosenblatt
    Pages 117-139
  6. Murray Rosenblatt
    Pages 141-154
  7. Murray Rosenblatt
    Pages 155-210
  8. Back Matter
    Pages 211-246

About this book


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 but elegant result of Cheng is also given that specifies conditions for the identifiability of the filter coefficients that specify a linear non-Gaussian random field.


Covariance matrix Gaussian Linear Time Series Likelihood Linear Time Series Probability theory Time series Variance

Authors and affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSan Diego La JollaUSA

Bibliographic information

  • Book Title Gaussian and Non-Gaussian Linear Time Series and Random Fields
  • Authors Murray Rosenblatt
  • Series Title Springer Series in Statistics
  • DOI
  • Copyright Information Springer-Verlag New York, Inc. 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-98917-4
  • Softcover ISBN 978-1-4612-7067-6
  • eBook ISBN 978-1-4612-1262-1
  • Series ISSN 0172-7397
  • Edition Number 1
  • Number of Pages XIII, 247
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
    Statistical Theory and Methods
  • Buy this book on publisher's site
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From the reviews:


"...will make this book useful as a reference source to the more theoretical among time series specialists."


"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."