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Strong convergence of estimators in nonlinear autoregressive models

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  • Liebscher, Eckhard

Abstract

In the paper we prove rates of strong convergence of M-estimators for the parameters in a general nonlinear autoregressive model. In the proofs we utilize a variational principle from stochastic optimization theory which was proved by Shapiro (Ann. Oper. Res. 30 (1991) 169). The application of the general theory is illustrated in the case of continuous threshold models.

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  • Liebscher, Eckhard, 2003. "Strong convergence of estimators in nonlinear autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 247-261, February.
    • Handle: RePEc:eee:jmvana:v:84:y:2003:i:2:p:247-261
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    References listed on IDEAS

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    1. K. S. Chan & H. Tong, 1986. "On Estimating Thresholds In Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 179-190, May.
    2. Potscher, Benedikt M. & Prucha, Ingmar R., 1986. "A class of partially adaptive one-step m-estimators for the non-linear regression model with dependent observations," Journal of Econometrics, Elsevier, vol. 32(2), pages 219-251, July.
    3. Koul, Hira L. & Zhu, Zhiwei, 1995. "Bahadur-Kiefer representations for GM-estimators in autoregression models," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 167-189, May.
    4. Huang, Sun Young & Basawa, I. V., 1994. "Large sample inference based on multiple observations from nonlinear autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 127-140, January.
    5. Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
    6. Liebscher, Eckhard, 1996. "Strong convergence of sums of [alpha]-mixing random variables with applications to density estimation," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 69-80, December.
    7. Liese, F. & Vajda, I., 1994. "Consistency of M-Estimates in General Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 93-114, July.
    8. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    9. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    10. Arcones, Miguel A., 1994. "Some strong limit theorems for M-estimators," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 241-268, October.
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    Cited by:

    1. Kaiyu Liang & Yong Zhang, 2024. "Almost Sure Central Limit Theorem for Error Variance Estimator in Pth-Order Nonlinear Autoregressive Processes," Mathematics, MDPI, vol. 12(10), pages 1-16, May.
    2. Joseph Ngatchou-Wandji & Madan L. Puri & Michel Harel & Echarif Elharfaoui, 2019. "Testing nonstationary and absolutely regular nonlinear time series models," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 557-593, October.

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