Bootstrapping Daily Returns

A daily log-return can be regarded as a test statistic - specifically the (unscaled) sample mean of a sequence of intraday random variables. We discuss sufficient conditions for a dependent bootstrap to consistently and non-parametrically estimate the entire distribution of this “test statistic”, up to, but not including, the location parameter. The method proposed is robust to market microstructure effects. There are many possible applications. In this paper, two are considered: 1) Estimating daily variance, and 2) Estimating Value-at-Risk (VaR). Of particular import: the VaR estimator is combined with the framework described in Patton & Li (2013) to produce forecast evaluation tests that are significantly more powerful than current popular techniques