Strong convergence of estimators in nonlinear autoregressive models

Authors:
Eckhard Liebscher
Affiliations:
Technical University Ilmenau, Institute of Mathematics, Ilmenau/Thür D-98684, Germany
Venue:
Journal of Multivariate Analysis
Year:
2003

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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.