Model-based clustering using finite mixture models for financial time series
Mixture models have been of intensive interest for the researchers over the last decade. The statistical models which are based on finite mixture distributions capture a lot of specific properties of the real data such as multicollinearity, skewness,kurtosis and unobserved heterogeneity. Mixture models frequently are also referred as semi-parametric models as their flexibility allow to approximate non-parametric problems.
Computationally intensive methods such as Markov Chain Monte Carlo methods and Expectation-Maximization algorithm must be considered. The Bayesian approach using MCMC methods in order to estimate the parameters of interest allows us to transform the complex structure of the mixture model into a set of simple structures using latent variables.
After exploring the existing computational tools for Bayesian inference for finite mixture models, I plan to keep the center of gravity of my research around model-based clustering using mixture models for financial time series. In particular the research question will aim to evaluate the existence of the link between the stock prices' volatility and different sources of information like for example the unemployment rate etc. My purpose thus is to develop a realistic and testable model suitable to investigate such connection, taking in account "non informative" or "conventional" prior distributions depending on the statistical structure of the trial.