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Random Coefficient Autoregressive Models: An Introduction

  • Des F. Nicholls
  • Barry G. Quinn

Part of the Lecture Notes in Statistics book series (LNS, volume 11)

Table of contents

  1. Front Matter
    Pages I-V
  2. Des F. Nicholls, Barry G. Quinn
    Pages 1-14
  3. Des F. Nicholls, Barry G. Quinn
    Pages 15-39
  4. Des F. Nicholls, Barry G. Quinn
    Pages 40-58
  5. Des F. Nicholls, Barry G. Quinn
    Pages 59-80
  6. Des F. Nicholls, Barry G. Quinn
    Pages 81-97
  7. Des F. Nicholls, Barry G. Quinn
    Pages 98-123
  8. Des F. Nicholls, Barry G. Quinn
    Pages 124-138
  9. Des F. Nicholls, Barry G. Quinn
    Pages 139-149
  10. Back Matter
    Pages 150-154

About this book

Introduction

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.

Keywords

Autoregressives Modell Hypothese Parameter Power Variance Zufall Zufallskoeffizient covariance matrix likelihood statistics

Authors and affiliations

  • Des F. Nicholls
    • 1
  • Barry G. Quinn
    • 2
  1. 1.Australian National UniversityCanberraAustralia
  2. 2.University of WollongongWollongongAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-6273-9
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90766-6
  • Online ISBN 978-1-4684-6273-9
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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