Nonparametric estimates for conditional quantiles of time series

摘要

We consider the problem of estimating the conditional quantile of a time series {Y_t} at time t given covariates X_t, where X_t can be either exogenous variables or lagged variables of Y_t . 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 is 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.