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.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Hurst Exponent, anti-persistence, fractal attractors, SDIC, chaos, inherent noise, market crashes, Renyi’s generalized fractal dimensions
• Subjects: G - Financial Economics > G1 - General Financial Markets; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; A - General Economics and Teaching > A1 - General Economics; G - Financial Economics > G0 - General > G01 - Financial Crises

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