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Neural network stochastic differential equation models with applications to financial data forecasting

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  • Luxuan Yang
  • Ting Gao
  • Yubin Lu
  • Jinqiao Duan
  • Tao Liu

Abstract

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions are, first, we propose a model called L\'evy induced stochastic differential equation network, which explores compounded stochastic differential equations with $\alpha$-stable L\'evy motion to model complex time series data and solve the problem through neural network approximation. Second, we theoretically prove that the numerical solution through our algorithm converges in probability to the solution of corresponding stochastic differential equation, without curse of dimensionality. Finally, we illustrate our method by applying it to real financial time series data and find the accuracy increases through the use of non-Gaussian L\'evy processes. We also present detailed comparisons in terms of data patterns, various models, different shapes of L\'evy motion and the prediction lengths.

Suggested Citation

  • Luxuan Yang & Ting Gao & Yubin Lu & Jinqiao Duan & Tao Liu, 2021. "Neural network stochastic differential equation models with applications to financial data forecasting," Papers 2111.13164, arXiv.org, revised Nov 2022.
  • Handle: RePEc:arx:papers:2111.13164
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    References listed on IDEAS

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    1. Huang, Yan & Kou, Gang & Peng, Yi, 2017. "Nonlinear manifold learning for early warnings in financial markets," European Journal of Operational Research, Elsevier, vol. 258(2), pages 692-702.
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    Cited by:

    1. Song, Yi & Xu, Wei & Wei, Wei & Niu, Lizhi, 2023. "Dynamical transition of phenotypic states in breast cancer system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 627(C).

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