A. Abhyankar, L. S. Copeland, W. Wong, Uncovering Nonlinear Structure in Real-Time Stock-Market Indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100, Journal of Business & Economic Statistics, Vol. 15, No. 1 (Jan., 1997), pp. 1-14
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Abhyankar et al. (1997) studied this question.