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 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...

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...