Most-Recent Anchoring with Recurrent Ordering for Time Series Forecasting

Most long-term time-series forecasting models map the look-back window directly to the full horizon in a single pass. While efficient, this design does not explicitly identify which historical states are most relevant to different future segments or exploit what followed those states. Analog forecasting addresses this by retrieving past states similar to the present and using their observed continuations, but single nearest matches can be unreliable and overlapping patches may produce redundant candidates. We propose DuoTS, a Dual-Context Time Series forecasting model that uses retrieved evidence without relying on it exclusively. DuoTS first produces a base forecast with a parallel patch encoder and linear prediction head, then progressively refines it one future patch at a time. Each refinement combines two views: a current context that attends to recent tokens and captures the latest dynamics, and a detail context that provides distinct retrieved analogs together with their subsequent trajectories. Patch-wise refinement allows the model to balance these views across the forecast horizon and associate each future segment with evidence appropriate to its temporal distance from the present. Experiments on multiple real-world datasets show that DuoTS achieves state-of-the-art performance, while ablations confirm the contribution of each context. The refinement mechanism is also model-agnostic, requiring only an encoded look-back window and the future-patch position, and can therefore be integrated into existing forecasting models.

Reliable long-horizon time series forecasting is an important yet difficult problem. Trends and seasonality introduce complex temporal structure that challenges learning-based forecasting models. Differencing, which subtracts nearby past values to remove such structure, is the classical remedy, but its reliance on hand-picked orders and periods has kept it largely absent from recent deep architectures. We propose Adaptive Reversible Differencing (AdaRDiff), a generalized differencing approach that uses learnable weights to simplify the series through weighted differencing with previous time instants. This yields stabilized residuals on which forecasting is performed, after which the removed components are restored autoregressively to reconstruct the forecast, capturing trend and seasonality jointly through a single operator. This reconstruction admits a closed-form convolutional expression, which parallelizes on GPU and yields up to $33.7\times$ speedup over the naive recurrence. We furthermore rely on a two-phase training schedule that separates temporal structure discovery from reconstruction learning, as suggested by a theoretical analysis of the gradient when using a linear forecasting model. AdaRDiff attains state-of-the-art forecast accuracy across eight benchmarks spanning electricity, weather, traffic, and energy, at negligible parameter cost. Furthermore, it is designed as a plug-and-play module: integrating AdaRDiff improves eight diverse backbones, from linear models to Transformers, in the large majority of cases, by up to $25.9\%$ with a linear backbone and $18.3\%$ with iTransformer.

Recent studies on long-term time series forecasting have shown that simple linear models and MLP-based predictors can achieve strong performance without increasingly complex architectures. However, many competitive baselines still rely on structural priors such as frequency-domain modeling, explicit decomposition, multi-scale mixing, or sophisticated cross-variable interaction modules, while paying less attention to how simple temporal mappings should be trained and organized. In this paper, we propose STAIR, short for Stagewise Temporal Adaptation via Individualization and Residual Learning, a training paradigm for long-term time series forecasting that aims to unlock the capacity of simple temporal mapping models without introducing complex architectural modules. STAIR decomposes forecasting ability into three progressive stages: it first learns common temporal dynamics across variables through a shared temporal mapping, then adapts the shared model to each variable via channel-wise fine-tuning to capture variable-specific patterns, and finally complements the backbone with cross-variable information through residual learning. We further introduce Shared-to-Individual Fine-tuning and alpha-RevIN to mitigate the limitations of strict channel independence and the overly strong normalization prior induced by standard RevIN. This design gradually increases modeling flexibility while keeping the core temporal predictor as a shallow MLP in the main experiments, with linear variants analyzed separately. Experiments on nine long-term forecasting benchmarks show that STAIR matches or outperforms recent strong baselines while preserving a simple temporal backbone, providing a concise and effective modeling perspective for long-term time series forecasting.