We show that the Truncated Realized Variance (TRV) of a semimartingale asset price converges to zero when observations are contaminated by microstructure noises. Under the additive iid noise assumption, a central limit theorem is also proved. In consequence it is possible to construct a feasible...

We show that the Truncated Realized Variance (TRV) of a SemiMartingale (SM) converges to zero when observations are contaminated by noise. Under the additive i.i.d. noise assumption, a central limit theorem is also proved. In consequence it is possible to construct a feasible test allowing us to...