Title: Bayesian inference and prediction for high-frequency data using Particle Filtering
Abstract: Financial prices are usually modeled as continuous, often involving geometric Brownian motion with drift, leverage, and possibly jump components. An alternative modelling approach allows fi nancial observations to take discrete values when they are interpreted as integer multiples of a fi xed quantity, the ticksize, the monetary value associated with a single change in the asset evolution. These samples are usually collected at very high frequency, exhibiting diverse trading operations per seconds. In this context, the observables are modelled via the Skellam process, defi ned as the diff erence between two independent Poisson processes. The intensities of the Poisson processes are therefore modelled as functions of a stochastic volatility process, which is in turn described by a discretised Ornstein-Uhlenbeck AR(1) process. Posterior computations for model fitting and out-of-sample prediction are obtained by using Particle MCMC methods. In particular, a novel technique is presented, that allows for the joint update of the time-varying components and the other parameters of the model.