Nonparametric Statistical Inference of Value At Risk For Financial Time Series

The paper considers nonparametric estimation of Value at Risk (VaR) and associated standard error estimation for dependent financial return series. The presence of dependence affects the variance of the VaR estimates and has to be taken into consideration in order to obtain adequate assessment on their variation. As estimation procedure of the standard errors is proposed based on a assessment on their variation. As estimation procedure of the standard errors is proposed based on a kernel estimation of the spectral density of a derived series. The performance of the VaR estimators and the proposed standard error estimation procedure are evaluated by theoretical investigation, simulation of commonly used models for financial returns and empirical studies on real financial return series.