Neural network stochastic differential equation models with applications to financial data forecasting
This addresses forecasting of complex financial time series with big jumps, though it appears incremental as it combines existing neural network and stochastic differential equation approaches with Lévy processes.
The authors tackled chaotic financial time series forecasting by proposing a Lévy-induced stochastic differential equation network that uses neural networks to approximate drift and diffusion coefficients with α-stable Lévy motion, achieving improved accuracy in real financial data applications.
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 Lévy induced stochastic differential equation network, which explores compounded stochastic differential equations with $α$-stable Lévy 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 Lévy processes. We also present detailed comparisons in terms of data patterns, various models, different shapes of Lévy motion and the prediction lengths.