Overview
- Authors:
-
-
Des F. Nicholls
-
Australian National University, Canberra, Australia
-
Barry G. Quinn
-
University of Wollongong, Wollongong, Australia
Access this book
Other ways to access
Table of contents (8 chapters)
-
-
- Des F. Nicholls, Barry G. Quinn
Pages 1-14
-
- Des F. Nicholls, Barry G. Quinn
Pages 15-39
-
- Des F. Nicholls, Barry G. Quinn
Pages 40-58
-
- Des F. Nicholls, Barry G. Quinn
Pages 59-80
-
- Des F. Nicholls, Barry G. Quinn
Pages 81-97
-
- Des F. Nicholls, Barry G. Quinn
Pages 98-123
-
- Des F. Nicholls, Barry G. Quinn
Pages 124-138
-
- Des F. Nicholls, Barry G. Quinn
Pages 139-149
-
Back Matter
Pages 150-154
About this book
In this monograph we have considered a class of autoregressive models whose coefficients are random. The models have special appeal among the non-linear models so far considered in the statistical literature, in that their analysis is quite tractable. It has been possible to find conditions for stationarity and stability, to derive estimates of the unknown parameters, to establish asymptotic properties of these estimates and to obtain tests of certain hypotheses of interest. We are grateful to many colleagues in both Departments of Statistics at the Australian National University and in the Department of Mathematics at the University of Wo110ngong. Their constructive criticism has aided in the presentation of this monograph. We would also like to thank Dr M. A. Ward of the Department of Mathematics, Australian National University whose program produced, after minor modifications, the "three dimensional" graphs of the log-likelihood functions which appear on pages 83-86. Finally we would like to thank J. Radley, H. Patrikka and D. Hewson for their contributions towards the typing of a difficult manuscript. IV CONTENTS CHAPTER 1 INTRODUCTION 1. 1 Introduction 1 Appendix 1. 1 11 Appendix 1. 2 14 CHAPTER 2 STATIONARITY AND STABILITY 15 2. 1 Introduction 15 2. 2 Singly-Infinite Stationarity 16 2. 3 Doubly-Infinite Stationarity 19 2. 4 The Case of a Unit Eigenvalue 31 2. 5 Stability of RCA Models 33 2. 6 Strict Stationarity 37 Appendix 2. 1 38 CHAPTER 3 LEAST SQUARES ESTIMATION OF SCALAR MODELS 40 3.
Authors and Affiliations
-
Australian National University, Canberra, Australia
Des F. Nicholls
-
University of Wollongong, Wollongong, Australia
Barry G. Quinn
