## $$S$$-estimation of nonlinear regression models with dependent and heterogeneous observations.(English)Zbl 0998.62060

Summary: In time series regression, where a single outlier can appear in the regressor vector multiple times due to the presence of lagged variables, resistance of an estimator to outliers is of serious concern. We show that the high resistance of $$S$$-estimators in cross section regression carries over to time series. We investigate the large sample properties of $$S$$-estimators in nonlinear regression with dependent, heterogeneous data and conduct Monte Carlo simulations to examine the performance of $$S$$-estimators and assess the accuracy of our asymptotic approximations. Finally, we offer a simple empirical example applying $$S$$-estimators to a financial time series.

### MSC:

 62J02 General nonlinear regression 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 65C05 Monte Carlo methods 62F35 Robustness and adaptive procedures (parametric inference) 62P20 Applications of statistics to economics

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