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

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