High frequency (or ultra high frequency) data cannot be used as continuous regularly sampled time series to build estimators of: volatility, traded volumes, correlations, etc...
The essential questions asked here are:
how to estimate volatility using HF data?
how to estimate correlations using HF data?
In terms of literature, the links usually pointed to are:
- The Rosenbaum-Robert approach, the price model with uncertainty zones is a model of trades and duration between trades (implicitly). It is worthwhile to try it.
- You can also use an Hawkes process, it will have the nice effect of capturing clustering effects on trades.
- if you want to use correlation / dependency measurements, you will face the Epps effect, so you should read at least one Yoshida paper on the topic.
- On order-flow viewpoint can be useful that for. There is a very good suite of papers by Rama Cont and Adrien de Larrad on this topic.
- Zhang et al. "Estimating Covariation: Epps Effect, Microstructure Noise" present a fairly straightforward way to effectively remove the Epps effect by considering a certain difference of correlations such that the Epps effect/ bias cancels.
- Market Microstructure knowledge needed to control an intra-day trading process.