Dynamic financial index models: Modeling conditional dependencies via graphs

Abstract

We discuss the development and application of dynamic graphical mod-els for multivariate financial time series in the context of Financial Index Models. The use of graphs generalizes the independence residual variation assumption of index models with a more complex yet still parsimonious alternative. Working with the dynamic matrix-variate graphical model framework, we develop general time-varying index models that are analytically tractable. In terms of methodol-ogy, we carefully explore strategies to deal with graph uncertainty and discuss the implementation of a novel computational tool to sequentially learn about the con-ditional independence relationships defining the model. Additionally, motivated by our applied context, we extend the DGM framework to accommodate random regressors. Finally, in a case study involving 100 stocks, we show that our pro-posed methodology is able to generate improvements in covariance forecasting and portfolio optimization problems. © 2011 International Society for Bayesian Analysis.