Time Series Forecasting with Ensembled Stochastic Differential Equations Driven by Lévy Noise

With the fast development of modern deep learning techniques, the study of dynamic systems and neural networks is increasingly benefiting each other in a lot of different ways. Since uncertainties often arise in real world observations, SDEs (stochastic differential equations) come to play an important role. To be more specific, in this paper, we use a collection of SDEs equipped with neural networks to predict long-term trend of noisy time series which has big jump properties and high probability distribution shift. Our contributions are, first, we use the phase space reconstruction method to extract intrinsic dimension of the time series data so as to determine the input structure for our forecasting model. Second, we explore SDEs driven by $\alpha$-stable L\'evy motion to model the time series data and solve the problem through neural network approximation. Third, we construct the attention mechanism to achieve multi-time step prediction. Finally, we illustrate our method by applying it to stock marketing time series prediction and show the results outperform several baseline deep learning models.