ARDM: Adaptive Residual Decay Mechanism for Dynamic Error Modification in Geophysical Time Series Forecasting

Multi-step time series forecasting is a fundamental problem across geoscientific applications, including meteorology, hydrology, climate analysis, and space and environmental sciences. A persistent challenge in such tasks is the progressive degradation of predictive accuracy as the forecast horizon increases. This phenomenon is primarily driven by the accumulation and temporal propagation of forecast errors, while most existing statistical and machine learning models lack explicit mechanisms to characterize, model, and correct the evolving dynamics of horizon-dependent residuals.

To address this limitation, we propose an adaptive error post-processing framework termed the Adaptive Residual Decay Mechanism (ARDM). ARDM is designed as an end-to-end predictive optimization strategy that enhances forecasting stability, robustness, and generalization across diverse temporal patterns and application scenarios. Rather than modifying the internal structure of forecasting models, ARDM operates as a residual-aware modification layer that can be seamlessly integrated with a wide range of statistical and machine-learning-based forecasting pipelines.

The proposed framework systematically integrates data preprocessing, initial multi-step forecasting, residual sequence construction, residual dependency modeling, dynamic error modification, and final output refinement. By explicitly constructing residual time series from preliminary forecasts, ARDM captures both short-term and long-term temporal dependencies in forecast errors, enabling structured modeling of error evolution across lead times. Within a symmetrical residual modeling architecture, a time-sensitive adaptive decay function is introduced to dynamically estimate and correct horizon-dependent forecast errors, allowing error adjustments to evolve consistently with increasing prediction horizons.

The decay function and its parameters are optimized through a joint multi-metric loss formulation evaluated across geoscientific and cross-domain time series forecasting datasets. This optimization strategy balances sensitivity to error magnitude with robustness to directional deviations, ensuring stable and reliable post-processing behavior, particularly for longer-range forecasts. Furthermore, ARDM systematically exploits historical residual information during the observation phase, enabling horizon-aware and dynamically consistent refinement of prediction errors through structured residual dependencies without increasing model complexity.

Extensive experiments conducted on multiple real-world geophysical time series datasets, including representative geomagnetic indices, demonstrate that ARDM consistently outperforms mainstream baseline statistical and machine learning methods across a range of standard evaluation metrics, including MAE, MSE, RMSE, MAPE, SSE, and the index of agreement (IA). Performance improvements are especially pronounced at longer prediction horizons, highlighting ARDM’s effectiveness in mitigating error accumulation in multi-step forecasting of geophysical processes. These results suggest that residual-aware, horizon-adaptive statistical post-processing provides a powerful and flexible pathway for improving the reliability of geophysical time series forecasting, with direct relevance to space weather and broader Earth system applications.