| LU Zudi,CHENG Ping.[J].数学年刊A辑,1999,20(2):173~184 |
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| NONPARAMETRIC IDENTIFICATION FOR NONLINEAR AUTOREGRESSIVE TIME SERIES MODELS: CONVERGENCE RATES |
| Received:December 15, 1997 Revised:September 03, 1998 |
| DOI： |
| 中文关键词: |
| 英文关键词:Nonlinear AR model, Optimal convergence rates, Kernel
approach,Autoregression function, Variance of white noise,
Consistency |
| 基金项目: |
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| 中文摘要: |
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| 英文摘要: |
| 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. |
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