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

Jul 16, 2026

Upload by Logic

Long-horizon multivariate time series forecasting remains difficult because non-stationarity, regime shifts, and compounding errors destabilize extrapolation. A Variability-Aware Recursive Neural Network (VARNN) was proposed to track variability using a residual-memory state driven by one-step prediction errors, but it was restricted to one-step sequence regression. StateFlow extends VARNN for long-horizon multi-step forecasting by building dual-state recurrent trajectories and using a chunk-based decoder plus two-stage optimization. Experiments on standard benchmarks show competitive results with compact recurrent modeling.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

Introduction

Problem of long-horizon multivariate forecasting

Limitations of transformer and conventional recurrent models

Extending VARNN and introducing StateFlow

arXiv :2607 .00197v1 [ cs .LG] 30 Jun 2026 STATEFLOW: DUAL-STATE RECURRENT MODELING FOR LONGHORIZON TIME SERIES FORECASTING Haroon Gharwi1* Yue Dai2* Kai Shu3+ *Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA +Department of Computer Science, Emory University, Atlanta, GA, USA [1](1 hgharwi@hawk.illinoistech.edu 2 ydai21@illinoistech.edu 3 kai.shu@emory.edu)[ hgharwi@hawk.illinoistech.edu](1 hgharwi@hawk.illinoistech.edu 2 ydai21@illinoistech.edu 3 kai.shu@emory.edu)[ 2](1 hgharwi@hawk.illinoistech.edu 2 ydai21@illinoistech.edu 3 kai.shu@emory.edu)[ ydai21@illinoistech.edu](1 hgharwi@hawk.illinoistech.edu 2 ydai21@illinoistech.edu 3 kai.shu@emory.edu)[ 3](1 hgharwi@hawk.illinoistech.edu 2 ydai21@illinoistech.edu 3 kai.shu@emory.edu)[ kai.shu@emory.edu](1 hgharwi@hawk.illinoistech.edu 2 ydai21@illinoistech.edu 3 kai.shu@emory.edu) 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) was recently introduced 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. Keywords— Time Series Forecasting, non-stationarity, residual learning, recurrent neural networks, distribution shift. 1 INTRODUCTION Long-horizon multivariate time series forecasting (LTSF) is a fundamental problem in applications such as energy demand prediction, traffic flow analysis, financial modeling, and environmental monitoring (Hyndman & Athanasopoulos, 2021; Brockwell & Davis, 2002; De Gooijer & Hyndman, 2006) . LTSF requires modeling extended temporal dependencies while remaining robust to non-stationarity, distribution shift, and evolving seasonal structure (Lim & Zohren, 2021; Baidya & Lee, 2024) . As the prediction horizon increases, modeling errors tend to accumulate, making stable long-term extrapolation particularly challenging (Lim et al., 2019; Oreshkin et al., 2020; Benidis et al., 2023) . Recent progress in LTSF has been largely driven by Transformer-based architectures that leverage self-attention to capture long-range dependencies. Patch-based tokenization strategies and channel-wise attention mechanisms have demonstrated strong empirical performance on standard benchmarks (Nie et al., 2023; Liu et al., 2024) . However, attention-based models generally exhibit quadratic complexity with respect to input length and often rely on global interaction patterns that may introduce computational overhead when long lookback windows are required. Recurrent architectures, in con

FAQs

What makes long-horizon multivariate time series forecasting challenging?

It is challenging due to non-stationarity, regime shifts, and error accumulation across prediction steps, which makes long-term extrapolation unstable.

How does StateFlow extend the original VARNN approach?

StateFlow extends VARNN to support long-horizon direct multi-step forecasting by using a dual-state recurrent backbone and mapping dual trajectories to the future horizon with a chunk-based decoder.

What two complementary signals does StateFlow capture from the lookback sequence?

It captures a hidden-state trajectory for primary temporal dynamics (trend, seasonality, level changes, recurring patterns) and a residual-memory trajectory for structured local prediction deviations driven by error transformations.

Jul 16, 2026

Upload by Logic