Channel-Dependent State Space Model for Multivariate Time Series Forecasting

Abstract

Multivariate time series forecasting (MTSF) is critical across many real-world domains. Existing deep learning approaches fall into two paradigms with distinct limitations: channel-independent (CI) methods unconditionally ignore cross-variable dependencies and model only temporal dynamics, while channel-dependent (CD) methods consider both but typically rely on architectural compromises to mitigate overfitting and computational overhead. We therefore propose Chameleon, a specialized CD state space model (SSM) that enables data-dependent, fine-grained interactions across variables while scaling linearly with their number. By connecting selective SSMs with the Kalman filter, we leverage the missing measurement update in the former for cross-variable modeling while preserving the SSM backbone for robust temporal modeling. We further identify favorable inductive biases of GatedDeltaNet for time series, adapt it as our backbone, and improve generalization through additional techniques, including a previously unexplored stochastic perturbation of reversible instance normalization. On strongly dependent ODE and PEMS datasets, Chameleon achieves the best MSE and MAE across all settings, while its CI ablation and prior CD methods incur 61-178% higher MSE on average. Across 28 standard benchmark settings, Chameleon also achieves better MSE and MAE than each baseline in at least 27 and 22 cases, respectively. Training-time and peak-memory analyses on Traffic and ETT further demonstrate competitive efficiency and favorable memory scalability across different variable counts.