Kalman-SSM: Modeling Long-Term Time Series With Kalman Filter Structured State Spaces

Abstract

In the field of time series forecasting, time series are often considered as linear time-varying systems, which facilitates the analysis and modeling of time series from a structural state perspective. Due to the non-stationary nature and noise interference in real-world data, existing models struggle to predict long-term time series effectively. To address this issue, we propose a novel model that integrates the Kalman filter with a state space model (SSM) approach to enhance the accuracy of long-term time series forecasting. The Kalman filter requires recursive computation, whereas the SSM approach reformulates the Kalman filtering process into a convolutional form, simplifying training and enhancing model efficiency. Our Kalman-SSM model estimates the future state of dynamic systems for forecasting by utilizing a series of time series data containing noise. In real-world datasets, the Kalman-SSM has demonstrated competitive performance and satisfactory efficiency in comparison to state-of-the-art (SOTA) models.