Observer state space models improve time series forecasting accuracy
Correct then Forecast: Observer State-Space Models for Time Series Forecasting
Machine Learning
Summary
Forecasting future values in time series data is hard because models usually rely on recent observations to predict next steps, but those observations are missing when forecasting ahead. The authors propose a new type of model called Observer State-Space Models (OSSMs) that treats observed data as measurements of an underlying system and separates updating predictions from using new data to correct the state estimate. This approach avoids problems when direct observations are unavailable and improves forecast accuracy on benchmark tests. The work connects ideas from control theory to modern forecasting models.
What this means in practice
- •For data science teams: Produce more accurate forecasts by correcting latent states with measurements instead of treating observations as direct inputs.
- •For signal processing engineers: Incorporate control-theoretic observer principles in time series models to reliably estimate system state over time.
Authors
Alexis-Raja Brachet, Guillaume Clavier--Frémond, Abdelhakim Ziani, Pierre-Yves Richard, Céline Hudelot
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.