StateFlow: Dual-State Recurrent Modeling for Long-Horizon Time Series Forecasting

2026-06-30

AI Summary

This work addresses the performance degradation in long-term multivariate time series forecasting caused by non-stationarity, regime shifts, and error accumulation. To tackle these challenges, the authors propose StateFlow, a novel framework built upon an enhanced VARNN architecture featuring a dual-state recurrent structure that separately models global temporal dynamics and local prediction residuals. By integrating a residual memory mechanism with a chunked decoder, StateFlow enables efficient direct multi-step forecasting. The approach extends VARNN to long-horizon settings for the first time, introducing dual-trajectory modeling and a two-stage optimization strategy that preserves the simplicity of linear recurrent encoding while substantially improving accuracy. Extensive experiments demonstrate that StateFlow consistently outperforms state-of-the-art linear, RNN, CNN, and Transformer-based models on standard long-term time series forecasting benchmarks, achieving both superior performance and a compact architecture.

Abstract

Long-horizon multivariate time series forecasting (LTSF) remains challenging due to non-stationarity, regime shifts, and error accumulation. The Variability-Aware Recursive Neural Network (VARNN) is designed to track such variability by maintaining a residual-memory state driven by one-step prediction errors. However, its original formulation is limited to one-step sequence regression and does not directly support multi-step forecasting. In this work, we extend VARNN to long-horizon forecasting and introduce StateFlow, a recurrent forecasting framework that uses VARNN as a dual-state recurrent backbone to capture two complementary signals from the lookback sequence: a hidden-state trajectory representing primary temporal dynamics, including trend, seasonality, level changes, and recurring patterns, and a residual-memory trajectory representing structured local prediction deviations, driven from a nonlinear recurrent transformation of errors between one-step base predictions and observed values. A chunk-based decoder separately summarizes these trajectories and maps them to the future horizon for direct multi-step forecasting. We further employ a two-stage optimization strategy that first trains the VARNN encoder through a one-step base prediction objective to optimize the internal representations over the lookback sequence, and then trains a horizon-specific decoder for direct multi-step forecasting. Experiments on standard LTSF benchmarks show that StateFlow achieves competitive performance against strong linear, recurrent, convolutional, and Transformer-based baselines while preserving linear recurrent encoding and a compact model design.

Problem

• long-horizon time series forecasting
• non-stationarity
• regime shifts
• error accumulation
• multi-step forecasting

Innovation

• dual-state recurrent modeling
• residual-memory trajectory
• long-horizon forecasting
• chunk-based decoder
• two-stage optimization