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.

Springer Book Archives
Reviews

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."

Book Information
ISBN 9780387989174
Author Murray Rosenblatt
Format Hardback
Page Count 247
Imprint Springer-Verlag New York Inc.
Publisher Springer-Verlag New York Inc.