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Random Coefficient Autoregressive Models: An Introduction

An Introduction

  • Book
  • © 1982


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

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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.

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Table of contents (8 chapters)

Authors and Affiliations

  • Australian National University, Canberra, Australia

    Des F. Nicholls

  • University of Wollongong, Wollongong, Australia

    Barry G. Quinn

Bibliographic Information

  • Book Title: Random Coefficient Autoregressive Models: An Introduction

  • Book Subtitle: An Introduction

  • Authors: Des F. Nicholls, Barry G. Quinn

  • Series Title: Lecture Notes in Statistics

  • DOI:

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Softcover ISBN: 978-0-387-90766-6Published: 13 September 1982

  • eBook ISBN: 978-1-4684-6273-9Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VI, 154

  • Topics: Probability Theory and Stochastic Processes, Statistics, general

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