Nansde-net: A neural sde framework for generating time series with memory
This addresses a fundamental problem in scientific and engineering domains for researchers and practitioners needing to generate time series with memory, but it is incremental as it builds on existing Neural SDE frameworks.
The paper tackled the challenge of modeling time series with memory effects by proposing NA-noise, an Itô-process-based alternative to fractional Brownian motion, and developed NANSDE-Net, a generative model that matches or outperforms existing models like fractional SDE-Net in reproducing memory features on synthetic and real-world datasets.
Modeling time series with long- or short-memory characteristics is a fundamental challenge in many scientific and engineering domains. While fractional Brownian motion has been widely used as a noise source to capture such memory effects, its incompatibility with Itô calculus limits its applicability in neural stochastic differential equation~(SDE) frameworks. In this paper, we propose a novel class of noise, termed Neural Network-kernel ARMA-type noise~(NA-noise), which is an Itô-process-based alternative capable of capturing both long- and short-memory behaviors. The kernel function defining the noise structure is parameterized via neural networks and decomposed into a product form to preserve the Markov property. Based on this noise process, we develop NANSDE-Net, a generative model that extends Neural SDEs by incorporating NA-noise. We prove the theoretical existence and uniqueness of the solution under mild conditions and derive an efficient backpropagation scheme for training. Empirical results on both synthetic and real-world datasets demonstrate that NANSDE-Net matches or outperforms existing models, including fractional SDE-Net, in reproducing long- and short-memory features of the data, while maintaining computational tractability within the Itô calculus framework.