Published online by Cambridge University Press: 09 September 2016
The main contribution of this paper is to propose a bootstrap method for inference on integrated volatility based on the pre-averaging approach, where the pre-averaging is done over all possible overlapping blocks of consecutive observations. The overlapping nature of the pre-averaged returns implies that the leading martingale part in the pre-averaged returns are kn-dependent with kn growing slowly with the sample size n. This motivates the application of a blockwise bootstrap method. We show that the “blocks of blocks” bootstrap method is not valid when volatility is time-varying. The failure of the blocks of blocks bootstrap is due to the heterogeneity of the squared pre-averaged returns when volatility is stochastic. To preserve both the dependence and the heterogeneity of squared pre-averaged returns, we propose a novel procedure that combines the wild bootstrap with the blocks of blocks bootstrap. 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 blocks of blocks bootstrap improves the finite sample properties of the existing first order asymptotic theory. We use empirical work to illustrate its use in practice.
We would like to thank Ilze Kalnina, Kevin Sheppard and Neil Shephard for many useful comments and discussions. This work was supported by grants FQRSC-ANR and SSHRC. In addition, Ulrich Hounyo acknowledges support from CREATES - Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation, as well as support from the Oxford-Man Institute of Quantitative Finance. Finally, Nour Meddahi benefited from the financial support of the chair “Marché des risques et création de valeur” Fondation du risque/SCOR.