On the Bahadur representation of sample quantiles in some stationary multivariate autoregressive processes

It is shown here that Bahadur's [Ann. Math. Statist. (1966) 37, 577-580] almost sure (a.s.) asymptotic representation of a sample quantile for independent and identically distributed random variables holds under certain regularity conditions for a general class of stationary multivariate autoregressive processes. This yields the asymptotic (multi-) normality of the standardized forms of quantiles in autoregressive processes. Other useful applications will be considered in a subsequent paper.