BOOTSTRAPPING PRE-AVERAGED REALIZED VOLATILITY UNDER MARKET MICROSTRUCTURE NOISE
提出一种结合wild bootstrap和blocks of blocks bootstrap的新自助法，用于在存在市场微观结构噪声时对积分波动率进行推断，解决了传统方法在波动率时变时失效的问题。
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 k n -dependent with k n 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.