Spatio-temporal modeling of financial maps from a joint multidimensional scaling-geostatistical perspective

• We study the relationships between international stock markets during a number of extreme episodes.
• We construct financial maps by means of the multidimensional scaling technique.
• We use spatio-temporal geostatistics to model the dependencies in stock market returns.
• We attempt to find patterns in the stock exchange market returns.

Modeling the propagation of extreme financial episodes and their consequences is currently a hot topic in international financial literature. This article focuses on the propagation of such episodes among the top stock exchange indexes in the world. Recent developments in spatio-temporal geostatistics are used to model this propagation process. However, as physical distance does not matter in the propagation of stock exchange returns, a multidimensional scaling of those returns is carried out to substitute the physical space with a financial one (a financial map). This process yields a set of financial-temporal coordinates which enable the use of the recent developments in spatio-temporal geostatistics. The way either extremely positive or extremely negative news propagates among the main stock exchanges in the world is a key factor for investors, financial experts and policy makers; it not only has important implications for portfolio management, policy-making, and risk assessment, but is also central to managing financial panic episodes.This combined multidimensional scaling/spatio-temporal geostatistics methodology has been applied to a database containing financial information about a set of 7 extreme episodes in the 29 most important stock exchange markets in the world. Results indicate that this combined methodology captures the propagation of returns in crashes better than in booms. Another interesting feature of this methodology is that it can be easily implemented in an expert system where the inputs are daily observed returns and the outputs are short-term predictions about those returns in an extreme episode, when financial propagation becomes financial contagion.