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This research explores the reliability of deep learning, specifically LongShort-Term Memory (LSTM) networks, for estimating the Hurst parameter infractional 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 fastgeneration of extensive datasets for fBm and fOU to train the LSTM network on alarge volume of data in a feasible time. The study analyses the accuracy of theLSTM network's Hurst parameter estimation regarding various performancemeasures like RMSE, MAE, MRE, and quantiles of the absolute and relativeerrors. It finds that LSTM outperforms the traditional statistical methods inthe case of fBm and fOU processes; however, it has limited accuracy on lfsmprocesses. The research also delves into the implications of training lengthand valuation sequence length on the LSTM's performance. The methodology isapplied by estimating the Hurst parameter in Li-ion battery degradation dataand obtaining confidence bounds for the estimation. The study concludes thatwhile deep learning methods show promise in parameter estimation of fractionalprocesses, their effectiveness is contingent on the process type and thequality of training data.

Deep learning the Hurst parameter of linear fractional processes and assessing its reliability