Estimation and Testing for Dependence in Market Microstructure Noise

Bias-corrected realized variance under dependent microstructure noise

“…The present section discusses the new methodology that allows for the selection of the appropriate lag J, based on the testing procedure proposed in Ubukata and Oya [7]. An alternative IV estimator which utilizes a different bias-correction method from the extended TSRV is also briefly introduced.…”

“…Ubukata and Oya [7] proposed an unbiased and consistent estimator of the microstructure noise autocovariance γ η (ℓ), and derived its asymptotic properties. The test statistic of the null hypothesis γ η (ℓ) = 0 is also applied to examine the significance of the microstructure noise dependence.…”

“…Reference can be made to Ubukata and Oya [7] for more details including the explicit formulation ofω ℓ .…”

“…The estimations proposed in previous studies ultimately require prior knowledge about this noise dependency, which needs to be rather estimated. The present study addresses these estimation issues and uses the consistent cross-covariance and autocovariance estimators of microstructure noise, and the tests statistics developed by Ubukata and Oya [7] to identify the noise dependence structure. The selection procedure of time scales based on Aït-Sahalia et al [1]'s Two Scales RV (TSRV) is also provided under the general conditions of dependent noise.…”

“…Section 3 discusses the realized variance and related estimators are given. Section 4 provides a brief review of the autocovariance estimator of microstructure noise proposed by Ubukata and Oya [7] followed by a discussion of of the selection two-scales TSRV estimator and alternative bias-corrected RV estimator. Section 5 presents the results of Monte Carlo simulation for the finite sample properties of the proposed selection procedure and the new bias-corrected estimator under the general noise dependence.…”