OSVIF: Order-Spectral Variable Interaction Framework for General Multivariate Time Series Analysis

Cross-variable dependencies in multivariate time series involve variable combinations of different sizes. These combinations can provide distinct information for characterizing a target variable and contribute jointly through cross-scale synergies. The roles of both combination information and these synergies vary across target variables. However, existing methods often mix information from combinations of different sizes or use constructed group structures to represent only a subset of combinations separately. This organization makes it difficult to preserve distinct representations of combination information by size, limiting the modeling of this information and its cross-scale synergies, as well as its selective use for different target variables. Consequently, cross-variable dependencies remain insufficiently characterized, limiting performance on downstream time series analysis tasks. To address these limitations, we propose OSVIF (Order-Spectral Variable Interaction Framework), a general framework for multivariate time series analysis. For each target variable, OSVIF covers all variable combinations and uses two spectra to link the organization of combination information by size with the modeling of cross-scale synergies. The natural order spectrum covers all source-variable combinations, preserves distinct representations by size, and applies target conditioning to form order-specific states. The natural coalition spectrum covers all combinations formed from these order-specific states and the state of the target variable itself, modeling how information from combinations of different sizes contributes synergistically to the characterization of the target variable. Both spectra use generating polynomials to cover their respective combination spaces in full without enumerating individual combinations, keeping computational costs manageable. By combining full combination coverage with distinct representations by size, OSVIF enables the selective use of combination information for each target variable and captures cross-scale synergies. It provides a unified variable interaction backbone for five tasks: long-term forecasting, short-term forecasting, imputation, classification, and anomaly detection. Experiments on 35 benchmark datasets show that OSVIF achieves strong performance across all five tasks, demonstrating its effectiveness and generality.