Definition of complex Hurst and fractional analysis for stock market fluctuation

Abstract

Hurst model has received significant interest in recent years and are being increasingly used to explain the stochastic phenomenon with long term dependency such as stock market fluctuations. Different from existing methods in traditional integer dimension construction, this paper proposes a novel fractional dimension derivation along with the exact algorithm involving the fractional norm definition and the fractional center moment extension, which ends up a complex Hurst parameter. The proposed algorithm provides more granularities in terms of the norm and the center moment that eventually leading to the detail revealing of the underline stock marketing drivers from both real and imaginary angles. The calculation results demonstrate that the complex model is able to distinguish the subtle difference between the stock market performances for the same field that the real model may overlook. We take the e-commence cluster of online related companies as an example.