Empirical Value at Risk for Weak Dependent Random Variables

Abstract

In this work, we study the empirical estimator of the Value at Risk (VaR for short) for weak dependent observations. Our approach uses the oscillation of the empirical process under hypothesis of moment's inequality. We provide general conditions which ensure the convergence of  the empirical estimator of the VaR. We also prove  a central limit theorem (CLT)  for the difference. We perform some simulations for different sequences to illustrate our results. Finally, we apply the results for different sequences under assumptions of mixing or covariance.