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Random Coefficient Autoregressive Models: An Introduction An 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 stat...

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Bibliographic Details
Main Authors: Nicholls, D.F., Quinn, B.G. (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1982, 1982
Edition:1st ed. 1982
Series:Lecture Notes in Statistics
Subjects:
Statistics, General
Statistics 
Probability Theory And Stochastic Processes
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Introduction
  • 1.1 Introduction
  • 2 Stationarity and Stability
  • 2.1 Introduction
  • 2.2 Singly-Infinite Stationarity
  • 2.3 Doubly-Infinite Stationarity
  • 2.4 The Case of a Unit Eigenvalue
  • 2.5 Stability of RCA Models
  • 2.6 Strict Stationarity 37 Appendix 2.1
  • 3 Least Squares Estimation of Scalar Models
  • 3.1 Introduction
  • 3.2 The Estimation Procedure
  • 3.3 Strong Consistency and the Central Limit Theorem
  • 3.4 The Consistent Estimation of the Covariance Matrix of the Estimates
  • 4 Maximum Likelihood Estimation of Scalar Models
  • 4.1 Introduction
  • 4.2 The Maximum Likelihood Procedure
  • 4.3 The Strong Consistency of the Estimates
  • 4.4 The Central Limit Theorem
  • 4.5 Some Practical Aspects
  • 5 A Monte Carlo Study
  • 5.1 Simulation and Estimation Procedures
  • 5.2 First and Second Order Random Coefficient Autoregressions
  • 5.3 Summary
  • 6 Testing the Randomness of the Coefficients
  • 6.1 Introduction
  • 6.2 The Score Test
  • 6.3 An Alternative Test
  • 6.4 Power Comparisons 108 Appendix 6.1
  • 7 The Estimation of Multivariate Models
  • 7.1 Preliminary
  • 7.2 The Least Squares Estimation Procedure
  • 7.3 The Asymptotic Properties of the Estimates
  • 7.4 Maximum Likelihood Estimation
  • 7.5 Conclusion
  • 8 An Application
  • 8.1 Introduction
  • 8.2 A Non-Linear Model for the Lynx Data
  • References
  • Author And Subject Index

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