The estimation of the daily integrated variance of the returns of financial assets is important task for pricing the derivatives of financial asset and risk management. It is well known that a realized variance (RV) is the simplest estimator of the daily integrated variance (IV). It is important that RV is badly biased estimator where the equilibrium price process is contaminated with the market microstructure noise. The microstructure noise is induced by various market frictions such as bid-ask bounces and the discreteness of price changes. There are three approaches to cope with the noise contamination: (i) use of the returns on the proper length of intervals based on optimal sampling frequency proposed by Bandi and Russell(2008a), (ii) subsampling and bias correction proposed by Zhang et al.(2005) and (iii) kernel estimation by Barndorff-Nielsen, et al.(2008). McAleer and Medeiros(2008) extensively review the recent RV literature. The key which ensures unbiasedness and consistency of IV estimator in the presence of market microstructure noise is the time dependence structure of the noise. All three approaches mentioned above eventually require the knowledge of the dependence structure. To identify the dependence structure, Ubukata and Oya(2009) have proposed consistent cross and autocovariance estimators and test statistics for the statistical significance. In this study, we propose the selection procedure of two time scales for TSRV by Ait-Sahalia et al.(2006) under general noise dependence structure applying the statistical inference proposed by Ubukata and Oya(2009). Further an alternative bias corrected IV estimator is also proposed. We conduct a series of Monte Carlo simulation to compare the bias and root mean squared error of the proposed estimator with TSRV and confirm that the proposed estimator has relatively small MSE and the proposed selection method of two time scales works well. Denote the extended TSRV and its bias adjusted one with the selected lags ((J) over cap, (K) over cap) through the procedure proposed by Ubukata and Oya (2009) as RV((J) over cap, (K) over cap) and RV((J) over cap, (K) over cap)((adj)), respectively. RV((K) over cap)((bc)) is the proposed bias corrected estimator with the selected lag (K) over cap. In the AR(1) noise dependence case, the empirical distributions of RV (J) over cap, (K) over cap and RV((J) over cap, (K) over cap)((adj)) are skew to the right. On the other hand, the skewnesses of the empirical distribution for i.i.d. and MA noise dependence cases are not severe. The empirical distribution of the proposed estimator RV((K) over cap)((bc)) is closer to symmetric than others when the noise dependence is strong. The bias and RMSE of estimators are reported in Table 1. The bias of RV((K) over cap)((bc)) is generally smaller than those of RV((J) over cap, (K) over cap) and RV((J) over cap, (K) over cap)((adj)). The RMSE is almost same for all cases except the strong noise dependence case. These simulation result suggests that the extended TSRV and its bias adjusted one with selected ((J) over cap, (K) over cap) and the proposed estimator RV((K) over cap)((bc)) are robust to the dependence of microstructure noise.
