Estimation of Random Coefficient Autoregressive Model with Error in Covariates

Measurement error is common in many statistical problems and has received considerable attention in various regression contexts. In this study, we consider the random coefficient autoregressive model with measurement error possibly present in covariates. The least squares and weighted least squares methods are used to estimate the model parameters, and the consistency and asymptotic normality of the two kinds of estimators are proved. Furthermore, we propose an empirical likelihood method based on weighted score equations to construct confidence regions for the parameters. The simulation results show that the weighted least squares estimators are superior to the least squares estimators and that the confidence regions have good finite-sample behavior. At last, the model is applied to a real data example.