Two-Scale Realized Variance Estimation with TSRV

Summary

The document asks how to adapt the two-scale realized variance estimator (TSRV) associated with high-frequency data. It proposes calculating realized variance at two subsampling intervals, then subtracting the shorter-scale estimate from the longer-scale estimate after adjusting by their effective sample sizes. The motivation is to reduce the impact of market microstructure noise in high-frequency observations.

The question contrasts this construction with the original TSRV approach, which combines a fast-scale estimate with an all-average estimate, and asks whether two fast scales are valid. It cites a paper’s suggested intervals for liquid stocks, but provides no answer, derivation, or empirical evidence establishing consistency for the proposed formula. The specific scale choices and validity therefore remain unresolved in the document and should not be treated as a confirmed estimator without consulting the underlying research.

Key ideas

• TSRV uses multiple sampling scales to estimate realized variance from high-frequency observations.
• The proposal subtracts a shorter-scale variance estimate from a longer-scale estimate with a sample-size adjustment.
• The document questions whether two fast scales can replace the original fast-scale and all-average combination.
• It offers no resolution or evidence that the proposed formula is consistent.

Tags

# Ultra high frequency TSRV


# Ultra high frequency TSRV












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?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.