Munich Personal RePEc Archive

Short-term Dependence in Time Series as an Index of Complexity: Example from the S&P-500 Index

Dominique, C-Rene and Rivera-Solis, Luis Eduardo (2012): Short-term Dependence in Time Series as an Index of Complexity: Example from the S&P-500 Index. Published in: International Business Research , Vol. Volume, No. No. 9 (8. August 2012): pp. 38-48.

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Abstract

The capital market is a reflexive dynamical input/output construct whose output (time series) is usually assessed by an index of roughness known as Hurst’s exponent (H). Oddly enough, H has no theoretical foundation, but recently it has been found experimentally to vary from persistence (H > 1/2) or long-term dependence to anti-persistence (H < 1/2) or short-term dependence. This paper uses the thrown-offs of quadratic maps (modeled asymptotically) and singularity spectra of fractal sets to characterize H, the alternateness of dependence, and market crashes while proposing a simpler method of computing the correlation dimension than the Grassberger-Procaccia procedure.

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