8. Multivariate financial series

Economic and financial globalization is increasing and accelerating interactions between the world's financial markets. Dependencies between several series can then be used, for example, to make arbitrage decisions. To do this, it is necessary to consider multivariate series (evolution of several stock prices, the values of several companies, etc.). This chapter outlines some of the elements needed to reason about this type of phenomenon. The two aspects that will be successively described are, on the one hand, multivariate GARCH models and volatility models and, on the other hand, co-integration, an extension of random walk, which accounts for several linked random trends.