On Evaluating Forecasts of Models for Realized Volatility

最近已经提出了几种方法在超高频金融文献中，以消除微观结构噪声的影响，并获得一致的估计综合波动率（IV）作为衡量事后每日波动率。即使是偏差校正和一致的已实现波动率（RV）估计IV可以包含残余的微观结构噪声和其他测量误差。这种噪声被称为“已实现波动率误差”。由于这些误差被忽略，我们在估计和预测IV时需要考虑到它们。本文通过Monte Carlo模拟研究了RV误差对用RV数据估算和预测IV的影响。发现：（i）忽略RV误差会导致估计量的严重偏差;（ii）当使用一致估计量时，并且当日内观测值的数量很大时，RV误差对一步前预报的影响很小;（iii）即使是最近文献中提出的部分校正的R^2，也应该被完全校正以评估预报。本文对R^2进行了全面的修正。标准普尔500指数数据的实证例子来证明本文开发的技术。

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.