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


  •  C-René Dominique    
  •  Luis Eduardo Rivera Solis    

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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