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Bayesian modelling of ultra high-frequency financial data

Golnaz Shahtahmassebi, Rana Moyeed, Paul Hewson


The availability of ultra high-frequency (UHF) financial data on transactions has revolutionised statistical modelling techniques in finance. The unique characteristics of such data, e.g. discrete structure of price change and unequally spaced time intervals have introduced new challenges to statistical studies. In this study, we develop a Bayesian framework for modelling integer-valued variables to capture the behaviour of price change. We propose the application of the zero inflated Poisson difference (ZPD) distribution and assess the effect of covariates. We apply our model to a set of FTSE100 index changes and obtain the predictive distribution of the index change. We then use the deviance information criterion for the purpose of model comparison. Finally, based on the probability integral transform, modified for the case of integer-valued variables, we show that our model is capable of explaining well the observed distribution of price change.


Ultra high-frequency; Bayesian; FTSE100 futures; integer-valued data; Poisson difference; zero inflated; MCMC; probability integral transform.

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