A note on cointegration of international stock market indices

Cointegration is frequently used to assess the degree of interdependence of financial markets. We show that if a stock's price follows a stock specific random walk, market indices cannot be cointegrated. Indices are a mere combination of n different random walks which itself is non-stationary by construction. We substantiate the theoretical propositions using a sample of 28 stock indices as well as a simulation study. In the latter we simulate stock prices, construct indices and test whether these indices are cointegrated. We show that while heteroscedasticity misleads cointegration tests, it is not sufficient to explain the high correlation between stock market index returns. A common random walk component and correlated price innovations are necessary to reproduce this feature.