ANOVA for diffusions and Ito processes

ANOVA for diffusions and Ito processes (2006)

by P A Mykland, L Zhang

Venue:

Ann. Statist

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Results 1 - 9 of 9

Ultra high frequency volatility estimation with dependent microstructure noise

by Yacine Aït-sahalia, Per A. Mykland, Lan Zhang

"... We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for tha ..."

Abstract - Cited by 30 (6 self) - Add to MetaCart

We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach based on multiple time scales, and compare empirically our different estimators to the standard realized volatility.

Edgeworth expansions for realized volatility and related estimators

by Lan Zhang, Per A. Mykland, Yacine Aït-sahalia , 2005

"... This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we derive Edgeworth expansions for such estimators. The expansions are developed in the framework of small-noise asymptotics. The results ..."

Abstract - Cited by 9 (3 self) - Add to MetaCart

This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we derive Edgeworth expansions for such estimators. The expansions are developed in the framework of small-noise asymptotics. The results have application to Cornish-Fisher inversion and help setting intervals more accurately than those relying on normal distribution.

Are Volatility Estimators Robust with Respect to Modeling Assumptions

by Yingying Li, Per A. Mykland - Bernoulli , 2007

"... We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel Q. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to smoothness conditions, the two scales realized volatility is rob ..."

Abstract - Cited by 9 (4 self) - Add to MetaCart

We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel Q. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to smoothness conditions, the two scales realized volatility is robust to the form of contamination Q. To push the limits of our result, we show what happens for some models that involve rounding (which is not, of course, smooth) and see in this situation how the robustness deteriorates with decreasing smoothness. Our conclusion is that under reasonable smoothness, one does not need to consider too closely how the microstructure is formed, while if severe non-smoothness is suspected, one needs to pay attention to the precise structure and also the use to which the estimator of volatility will be put.