On Evaluating Forecasts of Models for Realized Volatility

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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 realized volatility (RV) estimates of IV can contain residual microstructure noise and other measurement errors. Such noise is called "realized volatility error". As such errors are 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 ; (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 R^2 recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of R^2. An empirical example for S&P 500 data is used to demonstrate the techniques developed in the paper.