Date of Award


Degree Type


Degree Name

Master of Science in Statistics


Computer Science and Statistics

First Advisor

Gavino Puggioni


High-frequency data are observations collected at fine time scale. Such data largely incorporates pricing and transactions, of which institutional rules prevent from drastically rising or falling within a short period of time. This results in data changes based on the measure of one tick, a measure of the minimum upward or downward movement in the price of a security. The discreteness brings that the observations are in Z. A Skellam distribution has a unique property that returns values in Z.

We are interested in studying the Skellam process where the time-dependent intensities are Gaussian process. Such doubly stochastic Poisson process, also known as Cox process, is a point process which is a generalization of a Poisson process. We then investigate if this Skellam model provide better fit to high frequency financial data and how Gaussian process can capture the market microstructure.



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