Parameter estimation for generalized random coefficient autoregressive processes. (English) Zbl 0942.62102
Summary: A generalized random coefficient autoregressive (GRCA) process is introduced in which the random coefficients are permitted to be correlated with the error process. The ordinary random coefficient autoregressive process, the Markovian bilinear model and its generalization, and the random coefficient exponential autoregressive process, among others, are seen to be special cases of the GRCA process. Conditional least squares, and weighted least-squares estimators of the mean of the random coefficient vector are derived and their limit distributions are studied. Estimators of the variance-covariance parameters are also discussed. A simulation study is presented which shows that the weighted least-squares estimator dominates the unweighted least-squares estimator.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62F12 | Asymptotic properties of parametric estimators |
| 62M05 | Markov processes: estimation; hidden Markov models |
Keywords:
nonlinear time series; random coefficient autoregression; conditional least squares; weighted conditional leas squares; strong consistency; asymptotic normality; asymptotic relative efficiencyReferences:
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