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A Decomposition-based State Space Model for Multivariate Time-Series Forecasting

Shunya Nagashima, Shuntaro Suzuki, Shuitsu Koyama, Shinnosuke Hirano

TL;DR

DecompSSM tackles multivariate time series forecasting by explicitly decomposing each series into trend, seasonal, and residual components using three parallel GT-SSM branches with input-dependent timescales. A Global Context Refinement module propagates cross-variable information to re-synchronize components, while an Auxiliary Decomposition Loss enforces faithful reconstruction and component orthogonality, enabling end-to-end training. Empirical results across ECL, Weather, ETTm2, and PEMS04 show competitive and often superior forecasting performance against strong baselines, with notable gains on several horizons. The work highlights the value of component-wise state-space modeling coupled with global context and decomposition-aware objectives for robust, scalable multivariate forecasting, and points to future extensions such as automatic branch selection by frequency bands.

Abstract

Multivariate time series (MTS) forecasting is crucial for decision-making in domains such as weather, energy, and finance. It remains challenging because real-world sequences intertwine slow trends, multi-rate seasonalities, and irregular residuals. Existing methods often rely on rigid, hand-crafted decompositions or generic end-to-end architectures that entangle components and underuse structure shared across variables. To address these limitations, we propose DecompSSM, an end-to-end decomposition framework using three parallel deep state space model branches to capture trend, seasonal, and residual components. The model features adaptive temporal scales via an input-dependent predictor, a refinement module for shared cross-variable context, and an auxiliary loss that enforces reconstruction and orthogonality. Across standard benchmarks (ECL, Weather, ETTm2, and PEMS04), DecompSSM outperformed strong baselines, indicating the effectiveness of combining component-wise deep state space models and global context refinement.

A Decomposition-based State Space Model for Multivariate Time-Series Forecasting

TL;DR

DecompSSM tackles multivariate time series forecasting by explicitly decomposing each series into trend, seasonal, and residual components using three parallel GT-SSM branches with input-dependent timescales. A Global Context Refinement module propagates cross-variable information to re-synchronize components, while an Auxiliary Decomposition Loss enforces faithful reconstruction and component orthogonality, enabling end-to-end training. Empirical results across ECL, Weather, ETTm2, and PEMS04 show competitive and often superior forecasting performance against strong baselines, with notable gains on several horizons. The work highlights the value of component-wise state-space modeling coupled with global context and decomposition-aware objectives for robust, scalable multivariate forecasting, and points to future extensions such as automatic branch selection by frequency bands.

Abstract

Multivariate time series (MTS) forecasting is crucial for decision-making in domains such as weather, energy, and finance. It remains challenging because real-world sequences intertwine slow trends, multi-rate seasonalities, and irregular residuals. Existing methods often rely on rigid, hand-crafted decompositions or generic end-to-end architectures that entangle components and underuse structure shared across variables. To address these limitations, we propose DecompSSM, an end-to-end decomposition framework using three parallel deep state space model branches to capture trend, seasonal, and residual components. The model features adaptive temporal scales via an input-dependent predictor, a refinement module for shared cross-variable context, and an auxiliary loss that enforces reconstruction and orthogonality. Across standard benchmarks (ECL, Weather, ETTm2, and PEMS04), DecompSSM outperformed strong baselines, indicating the effectiveness of combining component-wise deep state space models and global context refinement.
Paper Structure (13 sections, 4 equations, 1 figure, 3 tables)

This paper contains 13 sections, 4 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Proposed Method
  4. Overview
  5. Input Embedding
  6. Gated-Time State Space Model
  7. Global Context Refinement Module
  8. Auxiliary Decomposition Loss
  9. EXPERIMENTS
  10. Setup
  11. Quantitative Results
  12. Ablation Study
  13. Conclusion

Figures (1)

  • Figure 1: Overview of DecompSSM. Left: decomposition-based forecasting with three GT-SSM branches (trend, seasonal, residual) and auxiliary objectives (orthogonality, reconstruction). Right: the Gated-Time SSM (GT-SSM) with the input-dependent Adaptive Step Predictor (ASP) built on S5smith_s5_2023.