A Comparison of Traditional and Deep Learning Methods for Parameter Estimation of the Ornstein-Uhlenbeck Process

TL;DR

This work tackles parameter estimation for the Ornstein–Uhlenbeck process, a common stochastic model in finance, physics, and biology. It compares traditional approaches like maximum likelihood estimation and Kalman-filter-based methods with a deep-learning solution using a multi-layer perceptron, trained on trajectories generated by Euler–Maruyama discretization to infer $(\mu,\theta,\sigma)$. Results show the MLP can achieve accurate parameter estimates and often outperforms classical methods when large datasets are available, with performance improving as data quantity increases. The findings support the potential of data-driven approaches to enhance real-time or large-scale estimation in stochastic systems, and point to future work exploring alternative architectures and noise settings.

Abstract

We consider the Ornstein-Uhlenbeck (OU) process, a stochastic process widely used in finance, physics, and biology. Parameter estimation of the OU process is a challenging problem. Thus, we review traditional tracking methods and compare them with novel applications of deep learning to estimate the parameters of the OU process. We use a multi-layer perceptron to estimate the parameters of the OU process and compare its performance with traditional parameter estimation methods, such as the Kalman filter and maximum likelihood estimation. We find that the multi-layer perceptron can accurately estimate the parameters of the OU process given a large dataset of observed trajectories and, on average, outperforms traditional parameter estimation methods.

Figures (2)

• Figure 1: Observed trajectories of the OU process.
• Figure 2: Average error of each method.