Bayesian non-parametric signal extraction for Gaussian time series

We consider the problem of unobserved components in time series from a Bayesian non-parametric perspective. The identification conditions are treated as unknown and analyzed in a probabilistic framework. In particular, informative prior distributions force the spectral decomposition to be in an identifiable region. Then, the likelihood function adapts the prior decompositions to the data. Bayesian analysis of unobserved components will be presented for financial high frequency data. Particularly, a three component model (long-term, intra-daily and short-term) will be analyzed to emphasize the importance and the potential of this work when dealing with the Value-at-Risk analysis. A second astronomical application will show how to deal with multiple periodicities.