Particular methods for the statistical analysis of mixtures of distributions and of hidden Markov chains

Predicting the weather, anticipating fluctuations in stock prices, assessing seismic risk… Although these tasks are very different, they all have one thing in common: time series analysis. The distinctive feature of these types of models is that the value of each observation depends on previously observed values. This makes time series analysis a powerful tool for describing chronological events, but up to a certain limit.
“These models can become so complex that it is sometimes difficult to integrate all the data streams, mainly due to data processing capability,” explains Dr. Jacob. The core aim of his research is to develop new effective methods based on an iterative selection of the most credible models, in order to predict the evolution of time series. In this respect, finance will be a key object of study.
My research focuses on Bayesian Inference in state space models, applications to stochastic volatility estimation and forecasting, model selection in time series, Monte Carlo methods.