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Gaussian and Non-Gaussian Linear Time Series and Random Fields

  • Murray Rosenblatt

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

Introduction

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.

Keywords

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

Authors and affiliations

  • Murray Rosenblatt
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaSan Diego La JollaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1262-1
  • Copyright Information Springer-Verlag New York, Inc. 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7067-6
  • Online ISBN 978-1-4612-1262-1
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site
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