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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.
Many electronic and acoustic signals can be modelled as sums of
sinusoids and noise. However, the amplitudes, phases and
frequencies of the sinusoids are often unknown and must be
estimated in order to characterise the periodicity or
near-periodicity of a signal and consequently to identify its
source. This book presents and analyses several practical
techniques used for such estimation. The problem of tracking slow
frequency changes over time of a very noisy sinusoid is also
considered. Rigorous analyses are presented via asymptotic or large
sample theory, together with physical insight. The book focuses on
achieving extremely accurate estimates when the signal to noise
ratio is low but the sample size is large. Each chapter begins with
a detailed overview, and many applications are given. Matlab code
for the estimation techniques is also included. The book will thus
serve as an excellent introduction and reference for researchers
analysing such signals.
Many electronic and acoustic signals can be modeled as sums of sinusoids and noise. However, the amplitudes, phases and frequencies of the sinusoids are often unknown and must be estimated in order to characterize the periodicity or near-periodicity of a signal and consequently to identify its source. Quinn and Hannan present and analyze several practical techniques used for such estimation. The problem of tracking slow frequency changes of a very noisy sinusoid over time is also considered. Rigorous analyses are presented via asymptotic or large sample theory, together with physical insight. The book focuses on achieving extremely accurate estimates when the signal to noise ratio is low but the sample size is large.
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