A note on self-weighted quantile estimation for infinite variance quantile autoregression models

This article focuses attention on quantile autoregressive (QAR) models in which the autoregressive coefficients can be dependent on the quantile function. We use the self-weighted quantile regressive estimation for infinite variance QAR models. The asymptotic normality of the estimated parameters are established conditionally on lagged values of the response. In addition, the Wald test statistics are developed for the linear restriction on the parameters. Finally, we discuss the regression rank score test and empirical likelihood method as alternative inference approaches, which do not require the estimations of nuisance parameters.