Random Coefficient Autoregressive Models: An Introduction:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1982
|
| Schriftenreihe: | Lecture Notes in Statistics
11 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (VI, 154 p) |
| ISBN: | 9781468462739 9780387907666 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4684-6273-9 |
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| 500 | |a 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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Datensatz im Suchindex
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| illustrated | Not Illustrated |
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| isbn | 9781468462739 9780387907666 |
| issn | 0930-0325 |
| language | English |
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| spelling | Nicholls, Des F. Verfasser aut Random Coefficient Autoregressive Models: An Introduction by Des F. Nicholls, Barry G. Quinn New York, NY Springer US 1982 1 Online-Ressource (VI, 154 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 11 0930-0325 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 Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Mathematik Statistik Quinn, Barry G. Sonstige oth https://doi.org/10.1007/978-1-4684-6273-9 Verlag Volltext |
| spellingShingle | Nicholls, Des F. Random Coefficient Autoregressive Models: An Introduction Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Mathematik Statistik |
| title | Random Coefficient Autoregressive Models: An Introduction |
| title_auth | Random Coefficient Autoregressive Models: An Introduction |
| title_exact_search | Random Coefficient Autoregressive Models: An Introduction |
| title_full | Random Coefficient Autoregressive Models: An Introduction by Des F. Nicholls, Barry G. Quinn |
| title_fullStr | Random Coefficient Autoregressive Models: An Introduction by Des F. Nicholls, Barry G. Quinn |
| title_full_unstemmed | Random Coefficient Autoregressive Models: An Introduction by Des F. Nicholls, Barry G. Quinn |
| title_short | Random Coefficient Autoregressive Models: An Introduction |
| title_sort | random coefficient autoregressive models an introduction |
| topic | Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Mathematik Statistik |
| topic_facet | Mathematics Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Mathematik Statistik |
| url | https://doi.org/10.1007/978-1-4684-6273-9 |
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