Nonparametric estimates for conditional quantiles of time series - Jürgen Franke; Peter Mwita; Weining Wang (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2014)
We consider the problem of estimating the conditional quantile of a time series fYtg at time t given covariates Xt, where Xt can ei- ther 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 uni- form 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.
Keywords: C00; C14; C50; C58; 330; Conditional quantile; kernel estimate; quantile autoregression; time series; uniform consistency; value-at-risk