This is the first paper about the high dimensional beta tests with high frequency financial data, which allowing that the number of regressors can be larger than the number of observations within each estimation block and can also grow to infinity in asymptotics. In this paper, the sum-type test...

This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we compute Edgeworth expansions for such estimators. Unlike the usual expansions, we have found that in order to obtain meaningful...

High-frequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We analyze the consequences of this dual feature of the data when estimating a continuous-time model. In particular, we measure the additional effects of the...

In this paper, we derive a new algebraic property of two scales estimation in high frequency data, under which the effect of sampling times is cancelled to high order. This is a particular robustness property of the two scales construction. In general, irregular, asynchronous, or endogenous...

We develop a principal component analysis (PCA) for high frequency data. As in Northern fairly tales, there are trolls waiting for the explorer. The first three trolls are market microstructure noise, asynchronous sampling times, and edge effects in estimators. To get around these, a robust...

In this paper, we provide non-parametric statistical tools to test stationarity of microstructure noise in general hidden Ito semimartingales, and discuss how to measure liquidity risk using high frequency financial data. In particular, we investigate the impact of non-stationary microstructure...

This research provides a theoretical foundation for our previous empirical finding that leverage effect has a role in estimating and forecasting volatility. This empirics is also related to earlier econometric studies of news impact curves (Engle and Ng, Chen and Ghysels). Our new theoretical...