Parameter Estimation of Long Memory Stochastic Processes with Deep Neural Networks

TL;DR

This paper introduces a deep learning approach using CNNs and LSTMs to accurately and efficiently estimate long memory parameters like the Hurst exponent in stochastic processes, outperforming traditional methods.

Contribution

It develops a novel neural network-based method for estimating long-range dependence parameters, trained on synthetic data, with superior accuracy and robustness over existing statistical techniques.

Findings

Neural estimators outperform traditional methods in accuracy.

Models demonstrate high speed and robustness.

Effective across multiple stochastic processes.

Abstract

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.