Classical and Bayesian Analysis of Dynamic
Correlation Models
Denis Pelletier
denis pelletier@ncsu.edu
Department of Economics
North Carolina State University
Box 8110
Raleigh, NC 27695-8110
USA
Abstract
In the first part of the talk, we propose a new model for the variance
between multiple time series, the Regime Switching Dynamic Correlation. We decompose the covariances into correlations and standard
deviations and the correlation matrix follows a regime switching model;
it is constant within a regime but different across regimes. The transitions between the regimes are governed by a Markov chain. This model
does not suffer from a curse of dimensionality and it allows analytic
computation of multi-step ahead conditional expectations of the variance matrix when combined with the ARMACH model [Taylor (1986)
and Schwert (1989)] for the standard deviations.
In the second part of the talk, we study the Bayesian analysis of
this type of models where we decompose the covariances into standard
deviations and correlations. We introduce strategies for eliciting prior
distributions on correlation matrices. They allow the introduction of
various types of structure while permitting the analytic evaluation of
the prior in terms of any hyperparameters it may depend on.