Can someone help if I am thinking correctly? If R(t,i)$R(t,i)$ is the i(th)i'th log-return for (for i = 1.....M)$i = 1\ldots,M$ of day t (for t = 1.....T)$t$ for $t = 1\ldots,T$.
Can I assume that the daily realized volatility (denoted RV(t)$RV(t)$) is a consistent estimateestimator of the true daily volatility denoted QV(t)$QV(t)$] in the sense that RV(t)--> QV(t)$RV(t)\rightarrow QV(t)$ when T--> ∞$T\rightarrow\infty$ ?