Random Coefficient Autoregressive Models: An Introduction: An Introduction

1 Introduction.- 1.1 Introduction.- Appendix 1.1.- Appendix 1.2.- 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.- Appendix 3.1.- Appendix 3.2.- 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.- Appendix 4.1.- Appendix 4.2.- 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.- 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.- Appendix 7.1.- 8 An Application.- 8.1 Introduction.- 8.2 A Non-Linear Model for the Lynx Data.- References.- Author And Subject Index.