A projected nonlinear state-space model for forecasting time series signals

Abstract

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy samples and predict future trajectories with uncertainty estimates while maintaining computational efficiency. Here, we propose a fast algorithm to learn and forecast nonlinear dynamics from noisy time series data. A key feature of the proposed model is kernel functions applied to projected lines, enabling fast and efficient capture of nonlinearities in the latent dynamics. Through empirical case studies and benchmarking, the model demonstrates its effectiveness in learning and forecasting complex nonlinear dynamics, offering a valuable tool for researchers and practitioners in time series analysis.

15 pages, 6 figures. International Journal of Forecasting, 2025

References in corpus (7)

• iTransformer: Inverted Transformers Are Effective for Time Series Forecasting
• N-BEATS: Neural basis expansion analysis for interpretable time series forecasting
• Variational Gaussian Process State-Space Models
• The low-rank hypothesis of complex systems
• Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC
• Learning interpretable continuous-time models of latent stochastic dynamical systems
• ODEFormer: Symbolic Regression of Dynamical Systems with Transformers