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

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  • Jacob Fein-Ashley

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.

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  • Jacob Fein-Ashley, 2024. "A Comparison of Traditional and Deep Learning Methods for Parameter Estimation of the Ornstein-Uhlenbeck Process," Papers 2404.11526, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2404.11526
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    1. R. H. Shumway & D. S. Stoffer, 1982. "An Approach To Time Series Smoothing And Forecasting Using The Em Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(4), pages 253-264, July.
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