# Parameter Estimation of Long Memory Stochastic Processes with Deep Neural Networks

arXiv: https://arxiv.org/abs/2410.03776 · HTML: https://mlsanity.com/paper/2410.03776/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 49 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Builds on (most cited first, 3 of 3)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)

## Built on by (most cited first, 2 of 2)

- [SigMA: Path Signatures and Multi-head Attention for Learning Parameters in fBm-driven SDEs](https://mlsanity.com/paper/2512.15088/) (2025)
- [NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process](https://mlsanity.com/paper/2607.11177/) (2026)

## Abstract (arXiv)

We present a purely deep neural network-based approach for estimating long memory parameters of time series models that incorporate the phenomenon of long-range dependence. Parameters, such as the Hurst exponent, are critical in characterizing the long-range dependence, roughness, and self-similarity of stochastic processes. The accurate and fast estimation of these parameters holds significant importance across various scientific disciplines, including finance, physics, and engineering. We harnessed efficient process generators to provide high-quality synthetic training data, enabling the training of scale-invariant 1D Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) models. Our neural models outperform conventional statistical methods, even those augmented with neural networks. The precision, speed, consistency, and robustness of our estimators are demonstrated through experiments involving fractional Brownian motion (fBm), the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process, and the fractional Ornstein-Uhlenbeck (fOU) process. We believe that our work will inspire further research in the field of stochastic process modeling and parameter estimation using deep learning techniques.