Value-at-Risk Inference with NN Sieve bootstrap

The aim of this paper is to construct bootstrap inference for VaR using a nonparametric bootstrap scheme, the NN-sieve bootstrap. This procedure, which retains the conceptual simplicity of the classical residual bootstrap, delivers consistent results for quite general nonlinear processes. In this paper, we consider stochastic volatility models for financial time series of the nonlinear autoregressive-ARCH type and, in this context, we prove the consistency of the conditional quantile function estimator and we derive its asymptotic distribution. The proposed procedure is also evaluated through a small Monte Carlo study. The results confirm that the bootstrap quantile estimators converge, in some sense, to a Normal distribution. Moreover their distibutions are centered around zero and the variability decreases when the sample size increases, supporting the consistency of the procedure.