Goncalves, Silvia, Hounyo, Ulrich and Meddahi, Nour (2014) Bootstrap Inference for Pre-averaged Realized Volatility based on Nonoverlapping Returns. Journal of financial econometrics, 12 (4). pp. 679-707.

Abstract

The main contribution of this article is to propose bootstrap methods for realized volatility-like estimators defined on pre-averaged returns. In particular, we focus on the pre-averaged realized volatility estimator proposed by Podolskij and Vetter (2009). This statistic can be written (up to a bias correction term) as the (scaled) sum of squared pre-averaged returns, where the pre-averaging is done over all possible nonoverlapping blocks of consecutive observations. Pre-averaging reduces the influence of the noise and allows for realized volatility estimation on the pre-averaged returns. The nonoverlapping nature of the pre-averaged returns implies that these are asymptotically uncorrelated, but possibly heteroskedastic. This motivates the application of the wild bootstrap in this context. We provide a proof of the first-order asymptotic validity of this method for percentile and percentile-t intervals. Our Monte Carlo simulations show that the wild bootstrap can improve the finite sample properties of the existing first-order asymptotic theory provided we choose the external random variable appropriately. We use empirical work to illustrate its use in practice.