Multivariate Time Series Modelling with Neural SDE Driven by Jump Diffusion

Neural stochastic differential equations (neural SDEs) are effective for modelling complex dynamics in time series data, especially random behavior. We introduced JDFlow, a novel normalizing flow method to capture multivariate structures in time series data. The framework involves a latent process driven by a neural SDE based on the Merton jump diffusion model. By using maximum likelihood estimation to determine the intensity parameter of the Poisson process in neural SDE, we achieved better results in generating time series data compared to previous methods. We also proposed a new approach to assess synthetic time series quality using a Wasserstein-based similarity measure, which compares signature cross-section distributions of original and generated time series.