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.
General
Imprint: |
Springer-Verlag New York
|
Country of origin: |
United States |
Series: |
Lecture Notes in Statistics, 11 |
Release date: |
September 1982 |
First published: |
1982 |
Authors: |
D F Nicholls
• B. G. Quinn
|
Dimensions: |
235 x 155 x 9mm (L x W x T) |
Format: |
Paperback
|
Pages: |
154 |
Edition: |
Softcover reprint of the original 1st ed. 1982 |
ISBN-13: |
978-0-387-90766-6 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Probability & statistics
|
LSN: |
0-387-90766-1 |
Barcode: |
9780387907666 |
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