Deep Neural Network Model for Hurst Exponent: Learning from R/S Analysis

Luca Di Persio and Tamirat Temesgen Dufera ()
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Luca Di Persio: Department of Computer Science, University of Verona, 37129 Verona, Italy
Tamirat Temesgen Dufera: Department of Applied Mathematics, Adama Science and Technology University, Adama P.O. Box 1888, Ethiopia

Mathematics, 2024, vol. 12, issue 22, 1-26

Abstract: This paper proposes a deep neural network (DNN) model to estimate the Hurst exponent, a crucial parameter in modelling stock market price movements driven by fractional geometric Brownian motion. We randomly selected 446 indices from the S&P 500 and extracted their price movements over the last 2010 trading days. Using the rescaled range (R/S) analysis and the detrended fluctuation analysis (DFA), we computed the Hurst exponent and related parameters, which serve as the target parameters in the DNN architecture. The DNN model demonstrated remarkable learning capabilities, making accurate predictions even with small sample sizes. This addresses a limitation of R/S analysis, known for biased estimates in such instances. The significance of this model lies in its ability, once trained, to rapidly estimate the Hurst exponent, providing results in a small fraction of a second.

Keywords: fractional Brownian motion; Hurst exponent; deep neural networks; R/S analysis; stock prices; DFA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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