Topic: Contributions on bootstrap inference Title: Bootstrapping integrated covariance matrix estimators in noisy jump-diffusion models with non-synchronous trading Authors:  Ulrich Hounyo - Aarhus University (Denmark) [presenting]
Abstract: We propose a bootstrap method for estimating the distribution (and functionals of it such as the variance) of various integrated covariance matrix estimators. We show the first-order asymptotic validity of the wild blocks of blocks bootstrap in the multivariate context with a potential presence of jumps, dependent microstructure noise, irregularly spaced and non-synchronous data. Our results justify using the bootstrap to estimate the covariance matrix of a broad class of covolatility estimators. The bootstrap variance estimator is positive semi-definite by construction, an appealing feature that is not always shared by existing variance estimators of the integrated covariance estimator. As an application of our results, we also consider the bootstrap for regression coefficients. We show that the wild blocks of blocks bootstrap, appropriately centered, is able to mimic both the dependence and heterogeneity of the scores. We provide a proof of construction of bootstrap percentile and percentile-$t$ intervals as well as variance estimates in this context. This contrasts with the traditional pairs bootstrap which is not able to mimic the score heterogeneity even in the simple case where no microstructure noise is present. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improves the finite sample properties of the alternative approach based on the Gaussian approximation. We illustrate its practical use on high-frequency equity data.