High frequency (HF) dynamics in financial distribution

Recently there has been an increasing interest in the statistical properties of the high frequency financial data related to the market micro-structural properties. High frequency econometrics is now well established after research on auto-regressive conditional duration models. In (HF) financial data, not only returns but also waiting times between consecutive trades are random variables. Compound Poisson processes are an instance of continuous time random walks (CTRW). In section two, (CTRW) theory is presented as applied to finance, and in section three a summary of the main results is presented.