Bayesian Modelling of Integer Data Using the Generalised Poisson Difference Distribution

摘要

Integer-valued random variables arising from the difference of two discrete variables can be seen frequently in various applications. In this paper, we obtain the distribution and derive the properties of the difference of two generalised Poisson variables with unequal parameters. This distribution is adopted to model a set of ultra high frequency (UHF) data relating to FTSE100 index futures using covariates. The unique characteristics of UHF data have introduced new theoretical and computational challenges to both statistical and financial studies. Such data consist of discrete-valued observations and unequally spaced time intervals. We also extend the model to its zero inflated version in order to capture the excess of zeros in the given data set. The analysis is carried out in a Bayesian framework using Markov Chain Monte Carlo methods. Various model diagnostics and model comparisons were undertaken which showed that index changes were explained well by the fitted model.