Bayesian Non-parametric Signal Extraction for Gaussian Time Series

Christian Macaro - Duke, SAMSI
Monday, November 16, 2009, 4:00 pm, Engineering 2 Building, Room 180
Hosted by Assistant Professor Pascale Garaud
Applied Mathematics & Statistics

Abstract

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.
    A full Bayesian analysis of unobserved components will be presented
for financial high frequency data. Particularly, a three component model
(long-term, intradaily 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.