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 efficient 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.