  This research explores the reliability of deep learning, specifically Long
Short-Term Memory (LSTM) networks, for estimating the Hurst parameter in
fractional stochastic processes. The study focuses on three types of processes:
fractional Brownian motion (fBm), fractional Ornstein-Uhlenbeck (fOU) process,
and linear fractional stable motions (lfsm). The work involves a fast
generation of extensive datasets for fBm and fOU to train the LSTM network on a
large volume of data in a feasible time. The study analyses the accuracy of the
LSTM network's Hurst parameter estimation regarding various performance
measures like RMSE, MAE, MRE, and quantiles of the absolute and relative
errors. It finds that LSTM outperforms the traditional statistical methods in
the case of fBm and fOU processes; however, it has limited accuracy on lfsm
processes. The research also delves into the implications of training length
and valuation sequence length on the LSTM's performance. The methodology is
applied by estimating the Hurst parameter in Li-ion battery degradation data
and obtaining confidence bounds for the estimation. The study concludes that
while deep learning methods show promise in parameter estimation of fractional
processes, their effectiveness is contingent on the process type and the
quality of training data.
