An Index of Co-Movements in Financial Time Series

Financial indices are constructed to capture the strong common variation in a large number of financial time series. Often, these measures are also of interest themselves since they can be related to important underlying economic concepts. We employ multivariate statistical theory to define indices that exploit the comovement with the data. Specifically, we advocate the use of the GLS representing portfolio obtained from the best (in the maximum likelihood series. We shoe that an index constructed in this way is robust to distribution assumptions and the true underlying structure of the data. We apply our techniques to construct a sensible new summary measure of exchange rate comovements. 

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