The LAD Estimation For Generalized Random Coefficient Autoregressive Model

Generalized random coefficient autoregressive model is an important nonlinear time series model, which is good in modeling the numerous dynamic economic, social and natural phenomena. Properties and parameters estimation of the model has been the hot issues. LAD estimation method is a robust estimation method, thus, the LAD estimation and asymptotic properties of the estimation is a problem worthy of study.In allusion to issues above, this literature use LAD estimation method, get the LAD estimation of parameters for generalized random coefficient autoregressive model and asymptotic properties of the estimation.Firstly, the paper structure parameters objective function of the parameter expectation for the generalized random coefficient autoregressive model. Then, we calculate the minimum value of the objective function and get the LAD estimation.according to the martingale central limit theorem and the ergodic theorem, we prove the asymptotic normality of the LAD estimation and give asymptotic normal confidence region. Then, above results are simulated by the Matlab.Secondly, the paper structure parameters objective function of the parameter variance and covariance vector for the generalized random coefficient autoregressive model. Then, we calculate the minimum value of the objective function and get the LAD estimation. according to the martingale central limit theorem and the ergodic theorem, we prove the asymptotic normality of the LAD estimation and give asymptotic normal confidence region. Then, above results are simulated by the Matlab.