# Andrea Cremaschi: Bayesian inference and prediction for high-frequency data using Particle Filtering

Andrea Cremaschi (earlier University of Kent, now UiO) will give a seminar in the lunch area, 8th floor Niels Henrik Abels hus at 14:15.

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 financial observations to take discrete values when they are interpreted as integer multiples of a fixed 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, defined as the difference 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.