To lag or not to lag? How to compare indices of stock markets that operate on different times

Financial markets worldwide do not have the same working hours. As a consequence, the study of correlation or causality between financial market indices becomes dependent on whether we should use all indices on the same day or lagged indices in computations of correlation matrices. The answer this article proposes is that we should consider both, by representing original and lagged indices in the same network. We then obtain a better understanding of how indices that operate on different hours relate to each other. We use a diverse range of 79 stock market indices from around the world and study their correlation structure, the eigenvalues and eigenvectors of their correlations under different time periods and volatility, as well as the differences between the working hours of the stock exchanges in order to analyze the possible time zone effects and suggest ways to remove them. We also analyze the enlarged correlation matrix obtained from original and lagged indices and examine a network structure derived from it, thus showing connections between lagged and original indices that could not be well represented before.