Correct then Forecast: Observer State-Space Models for Time Series Forecasting

2026-09-27

AI Summary

This study addresses the limitation of existing state-space models (SSMs) that directly inject observations into system dynamics, which causes abrupt shifts in dynamical mechanisms and modeling inconsistencies under missing data. To overcome this, we draw upon observer theory from control engineering to propose the Observer State-Space Model, which treats observations as measurements of an underlying autonomous system. By decoupling state propagation from measurement assimilation, our approach establishes a "correct-then-predict" paradigm and provides rigorous analyses of observability and convergence. This framework offers a unified interpretation of existing SSM architectures. Under identical parameter budgets and training configurations, the proposed method significantly outperforms baselines across multiple benchmarks.

Abstract

Time series forecasting requires extrapolating the dynamics of an observed process beyond the last available measurement. Yet recurrent forecasting models typically treat observations as inputs that directly control their latent dynamics. It leads to a regime change when these observations become unavailable at prediction time. Following a state-estimation perspective, we introduce Observer State-Space Models (OSSMs), a class of recurrent models that interprets the observed input time series as measurements of an underlying autonomous dynamical system. OSSMs explicitly separate latent-state propagation from measurement assimilation: a single transition governs the dynamics across both context and forecasting intervals, while available observations correct the estimated state through an observer. This formulation naturally exposes classical control-theoretic properties, including observability and convergence of the state estimation error. We further show that conventional and recent SSMs can be recovered as particular instances of our OSSM framework, thereby providing a unified interpretation of their recurrent dynamics and revealing modeling inconsistencies. We perform experiments across several benchmarks showing that OSSM achieves substantial improvements while maintaining the same parameter count and training setup as the corresponding SSM baseline. These results support a simple principle for recurrent forecasting: observations should correct the estimated latent state, rather than control the dynamics used to propagate it.

Problem

• time series forecasting
• state-space models
• recurrent models
• observer
• regime change

Innovation

• Observer State-Space Models
• Time Series Forecasting
• State Estimation
• Control Theory
• State-Space Models