Modeling discrete stock price changes using a mixture of Poisson distributions

We study discrete price changes due to the size of a trade in the market microstructure model. We use a mixture of Poisson distributions to model the discrete changes in stock price. The parameters are estimated using the Expectation–Maximization (EM) algorithm with mixing probabilities which depend on order size. Consistency and asymptotic normality of a sequence of estimators are proved, and asymptotic confidence intervals for functions of the parameters are derived. We test the method with simulated and real data.