NONPARAMETRIC IDENTIFICATION FOR NONLINEAR AUTOREGRESSIVE TIMESERIES MODELS： CONVERGENCE RATES

In this paper the optimal convergence rates of estimators ba~ed on kernel approach fornonlinear AR model are investigated in the sense of Stone[17‘1a]. By combining the mixingproperty of the stationary solution with the characteristics of the model itself, the restrictiveconditions in the literature which are not easy to be satisfied by the nonlinear AR model axeremoved, and the mild conditions are obtained to guarantee the optimal ratea of the estimatorof autoregTession function. In addition: the strongly coasistent estimator of the ~riance ofwhite noise is also constructed.

NONPARAMETRIC IDENTIFICATION FOR NONLINEAR AUTOREGRESSIVE TIME SERIES MODELS: CONVERGENCE RATES

In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone$^{[17,18]}$.By combining the $alpha$--mixing property of the stationary solution with the characteristics of the model itself, the restrictive conditions in the literature which are not easy to be satisfied by the nonlinear AR model are removed, and the mild conditions are obtained to guarantee the optimal rates of the estimator of autoregression function. In addition,the strongly consistent estimator of the variance of white noise is also constructed.