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

Christian Donner, Anuj Mishra and Hideaki Shimazaki

International Journal of Forecasting, 2025, vol. 41, issue 3, 1296-1309

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 the fast and efficient capture of nonlinearities in the latent dynamics. Through empirical case studies and benchmarking, the model demonstrates its effectiveness at learning and forecasting complex nonlinear dynamics, offering a valuable tool for researchers and practitioners in time series analysis.

Keywords: State space model; Filtering/smoothing; Nonlinear transition; Ridge kernel; Chaotic attractors (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:intfor:v:41:y:2025:i:3:p:1296-1309

DOI: 10.1016/j.ijforecast.2025.01.002

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