Estimating quadratic variation using realised volatility

This paper looks at some recent work on estimating quadratic variation using realised volatility (RV) - that is sums of M squared returns. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent estimator of quadratic variation (QV). We express concern that without additonal assumptions it seems difficult to given 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 volatility 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. We show that even with the large values of M and RV is sometimes a quite noisy estimator of integrated volatility