Nonparametric Estimates for Conditional Quantiles of Time Series

Abstract

We consider the problem of estimating the conditional quantile of a time series fYtg at time t given covariates Xt , where Xt can either exogenous variables or lagged variables of Yt . The conditional quantile is estimated by inverting a kernel estimate of the conditional distribution function, and we prove its asymptotic normality and uniform strong consistency. The performance of the estimate for light and heavy-tailed distributions of the innovations are evaluated by a simulation study. Finally, the technique is applied to estimate VaR of stocks in DAX, and its performance is compared with the existing standard methods using backtesting.