A Note on Cointegration of International Stock Market Indices

Abstract

Cointegration has frequently been used in the financial econometrics literature to assess the degree of interdependence of financial markets. We show that if individual stock prices are generated by random walks with possibly contemporaneously correlated innovations, the resulting indices cannot be cointegrated as they are a combination of n random walks which itself is non-stationary by construction. This result holds if (as in factor models) an additional common global or local random walk is allowed for. There will, however, never be less than n random walk components, as otherwise company specific characteristics would be ruled out to affect the stock price permanently. To substantiate the theoretical propositions we simulate stock prices (allowing for heteroscedasticity, correlated innovations and common factors), construct indices and test whether these indices are cointegrated. We show that while heteroscedasticity alone is able to mislead cointegration tests, it is not sufficient to explain at the same time the empirically found high correlation between stock market indices. A common stochastic factor as well as correlated price innovations are necessary to reproduce the empirical characteristic features. We conclude that cointegration is not a suitable method to analyze stock market interdependence.

Keywords: Cointegration, Random Walk, International Financial Markets

JEL Classification: C32, G15