Bootstrapping pre-averaged realized volatility under market microstructure noise
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.
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