Asymptotics of quantiles and rank scores in nonlinear time series

This paper extends the concept of regression and autoregression quantiles and rank scores to a very general nonlinear time series model. The asymptotic linearizations of these nonlinear quantiles are then used to obtain the limiting distributions of a class of L-estimators of the parameters. In particular, the limiting distributions of the least absolute deviation estimator and trimmed estimators are obtained. These estimators turn out to be asymptotically more ef®cient than the widely used conditional least squares estimator for heavy-tailed error distributions. The results are applicable to linear and nonlinear regression and autoregressive models including self-exciting threshold autoregressive models with known threshold