Kernel Conditional Quantile Estimation for Stationary Processes with Application to Conditional Value-at-Risk

The paper considers kernel estimation of conditional quantilesfor both short-range and long-range-dependent processes. Undermild regularity conditions, we obtain Bahadur representationsand central limit theorems for kernel quantile estimates ofthose processes. Our theory is applicable to many price processesof assets in finance. In particular, we present an asymptotictheory for kernel estimates of the value-at-risk (VaR) of themarket value of an asset conditional on the historical informationor a state process. The results are assessed based on a smallsimulation and are applied to AT&T monthly returns.