###### Exploring linkages between international stock markets using Graphical models for multivariate time series

Faculty of Mathematics and Statistics, UPC (Barcelona Tech)

MASTER in Advanced Mathematics and Mathematical Engineering

January, 2014

by **Gehlavij Mohammadi**

Supervisor: Argimiro Arratia

Abstract: In this Master of Science Project we apply graphical statistics models for analyzing causality relations among various international stock markets. We present Graphical models in terms of conditional independence in probability spaces, as opposed to conditional orthogonality of Hilbert spaces, which is the usual presentation of this theory in the literature. We introduce the concept of causality graph with weights to assess for the different degrees of causality relations among markets, i.e., causes coming far from the past are distinguish from causes from the most immediate past. We programmed the construction of causality graphs in R, and apply this methodology to a small sample of 3 major stock markets indices S & P 500, Nikkei 225 and FTSE 100 to trace the spillover of volatility between them. We repeat this experiment with 11 major stock indices representing industrialized as well as emerging markets all over the world.