Microstructure noise in the continuous case: The pre-averaging approach

Abstract

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Bootstrapping Pre-Averaged Realized Volatility Under Market Microstructure Noise

“…This has motivated the development of alternative estimators. One popular method is the pre-averaging approach first introduced by Podolskij and Vetter (2009) and further studied by Jacod et al (2009)…”

“…In this paper, we propose a bootstrap method that can be used to estimate the distribution and the variance of the pre-averaged realized volatility estimator of Jacod et al (2009). Our proposal is to resample the pre-averaged returns instead of resampling the original noisy returns.…”

“…When pre-averaging occurs over overlapping blocks of returns, as in Jacod et al (2009), the squared pre-averaged returns are k n -dependent, where k n denotes the block length of the interval over which the pre-averaging is done and n denotes the sample size. Since k n is proportional to √ n, k n → ∞ as n → ∞, which implies that the pre-averaged returns are strongly dependent.…”

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AbstractThe main contribution of this paper is to propose a bootstrap method for inference on integrated volatility based on the pre-averaging approach of Jacod et al (2009), where the pre-averaging is done over all possible overlapping blocks of consecutive observations. The overlapping nature of the pre-averaged returns implies that these are k n -dependent with k n growing slowly with the sample size n. This motivates the application of a blockwise bootstrap method.

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Obtaining and Predicting the Bounds of Realized Correlations

“…150 (3) To deal with the combination of both problems, methods such as subsampling , pre-averaging (Jacod et al, 2009) and the two-and multi-scales estimators (Zhang, 2011) have been proposed to restore consistency of the estimators. Voev and Lunde (2007) proposed a bias correction method for the Hayashi and Yoshida estimator in the presence of dependent microstructure noise while Nolte and Voev (2009) propose a least squares approach to obtain the unbiased integrated volatility or co-volatility.…”