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

ArXiv ID: 2404.11526 “View on arXiv”

Authors: Unknown

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.

Keywords: Ornstein-Uhlenbeck process, parameter estimation, multi-layer perceptron, Kalman filter, Maximum Likelihood Estimation, stochastic process

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents rigorous mathematical derivations of the OU process, discretization, and Kalman filter, scoring high on math complexity. While not featuring actual backtest results, the inclusion of experimental comparisons and detailed methodology pushes empirical rigor above average.

  flowchart TD
    A["Research Goal<br>Parameter Estimation of OU Process"] --> B{"Methodology"}
    B --> C["Traditional Methods<br>Kalman Filter & MLE"]
    B --> D["Deep Learning<br>Multi-Layer Perceptron"]
    B --> E["Dataset<br>Simulated OU Trajectories"]
    C --> F["Computational Process<br>Batch Estimation"]
    D --> F
    E --> F
    F --> G["Key Findings/Outcomes"]
    G --> H["MLP accurately estimates parameters"]
    G --> I["MLP outperforms traditional methods<br>on large datasets"]