I'd like to verify my approach to calculate high-frequency RV estimator, as introduced in Ait-Sahalia, Myklad, Zhang 2011. After reading the paper a couple of times, it seems to me, that the only difference to the original TSRV estimator is taking two "fast scales" instead one fast and one all-average, or am I missing something?
In other words, to take subsamples of length $J$ and then $K$, such that $1\leq J < K \leq n$ and where
$[Y, Y]^{J}_{T}=\frac{1}{J}\sum^{n-J}_{i=0}(Y_{t_{i+J}}-Y_{t_{i}})^{2}$
Then use this equation twice and arrive at:
$\widehat{<X,X>}^{(tsrv)} = [Y, Y]^{K}_{T} - \frac{\bar{n_{K}}}{\bar{n_{J}}}[Y, Y]^{J}_{T}$
which is consistent for suitable choices of J and K For liquid stocks the paper offers $J=1$ and $K=5$ minutes, respectively. Is my understanding correct, please?
