Several methods have recently been proposed in the ultra high frequency financial
literature to remove the effects of microstructure noise and to obtain consistent
estimates of the integrated volatility (IV) as a measure of ex-post daily volatility. Even
bias-corrected and consistent (modified) realized volatility (RV) estimates of the
integrated volatility can contain residual microstructure noise and other measurement
errors. Such noise is called "realized volatility error". As such measurement errors
ignored, we need to take account of them in estimating and forecasting IV. This paper
investigates through Monte Carlo simulations the effects of RV errors on estimating and
forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious
bias in estimators due to model misspecification; (ii) the effects of RV errors on
one-step ahead forecasts are minor when consistent estimators are used and when the
number of intraday observations is large; and (iii) even the partially corrected R2
recently proposed in the literature should be fully corrected for evaluating forecasts.
This paper proposes a full correction of R2, which can be applied to linear and nonlinear,
short and long memory models. An empirical example for S&P 500 data is used to
demonstrate that neglecting RV errors can lead to serious bias in estimating the model
of integrated volatility, and that the new method proposed here can eliminate the effects
of the RV noise. The empirical results also show that the full correction for R2 is
necessary for an accurate description of goodness-of-fit.
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