Estimating quadratic variation using realized variance
回顾了用已实现方差估计二次变差的基本结果，指出在一般半鞅模型下难以给出估计的不确定性度量，但在随机波动模型下可推导渐近分布，并用汇率和股票数据说明即使采样频率很高，估计仍可能很嘈杂。
Abstract This paper looks at some recent work on estimating quadratic variation using realized variance (RV)—that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high‐frequency financial return data. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent (as M → ∞) estimator of quadratic variation (QV). We express concern that without additional assumptions it seems difficult to give any measure of uncertainty of the RV in this context. The position dramatically changes when we work with a rather general SV model—which is a special case of the semimartingale model. Then QV is integrated variance and we can derive the asymptotic distribution of the RV and its rate of convergence. These results do not require us to specify a model for either the drift or volatility functions, although we have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data and some stock data. We show that even with large values of M the RV is sometimes a quite noisy estimator of integrated variance. Copyright © 2002 John Wiley & Sons, Ltd.