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

TL;DR

This paper introduces a neural network-based stochastic differential equation model using Le9vy processes for financial data forecasting, demonstrating improved accuracy and theoretical convergence guarantees.

Contribution

We propose a novel Le9vy induced stochastic differential equation network that models complex time series with jump properties and prove its numerical solution converges without curse of dimensionality.

Findings

Enhanced prediction accuracy with non-Gaussian Le9vy processes

Theoretical proof of convergence in probability

Effective modeling of chaotic time series with jumps

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.