demand planners

Abstract: Explicitly modeling periodicity has proven to be an efficient approach for time series forecasting, where the residual, obtained after removing the periodic component from the time series, is typically treated as unstructured noise. However, in this work, we show that such residuals still exhibit structured, \textit{phase-dependent} deviations, as supported by both empirical observations and theoretical analysis. This suggests that residuals should not be treated merely as unstructured noise, but instead as \textit{phase-conditioned signals} whose variations arise in both direction and magnitude. Motivated by this perspective and inspired by phase and amplitude modulation in classical signal processing, we propose \textit{Paloma}, a simple yet effective framework for modeling residual deviations. Specifically, Paloma comprises two complementary modules: \textit{a Phase Rotation module}, which performs phase-conditioned rotations to capture directional changes in the feature space, and \textit{an Amplitude Scaling module}, which applies phase-conditioned affine transformations to model magnitude variations. We further abstract the two modules into a general-purpose plugin, termed the \textit{Paloma technique}, which can be readily integrated into existing forecasting architectures to modulate input sequences in a phase-aware manner, enabling backbone models to capture phase-dependent variations in both direction and magnitude. Extensive experiments on twelve datasets demonstrate that Paloma achieves state-of-the-art and robust forecasting performance. Additional results show that the Paloma technique consistently improves a wide range of baseline models, validating its effectiveness as a general-purpose component. Our Code is available at \url{https://github.com/TSTS13/Paloma}.

Abstract: Time series foundation models are becoming increasingly popular for general-purpose forecasting. However, most leading models predict marginal quantiles, leaving the dependence structure of future trajectories unspecified. This distinction matters for trajectory-dependent quantities such as cumulative demand, peak load, and event timing, yet point and marginal scores do not reveal it. To model this dependence, we introduce PathFM, a trajectory-based forecasting model that uses flow matching to generate complete future paths. We further distill the model to one or two steps and share history attention cache across draws. Together, these enable PathFM to generate multiple paths for a single series in roughly the time needed for one query to a quantile model. The distilled sampler also makes it practical to optimize a calibration loss directly. PathFM achieves competitive marginal accuracy on the established forecasting benchmarks fev-bench and TIME. To complement these evaluations, we introduce Forecast Path Score Bench (fps-bench), which augments fev-bench tasks with energy and variogram scores and downstream metrics. PathFM achieves a higher aggregate path score on fps-bench than all evaluated external baselines. Experiments on chaotic systems further show that our flow model sustains long-run variability, while strong baselines rapidly collapse. PathFM makes generative time series forecasting both competitive and practical, enabling diverse downstream applications.

Abstract: Hierarchical time series forecasting requires generating accurate predictions that are coherent across multiple levels of aggregation. Existing methods either rely on two-stage pipelines with post-hoc reconciliation or on end-to-end models that often lack statistical guarantees. We introduce a unified framework that formulates hierarchical forecasting as a multivariate regression problem in a vector-valued reproducing kernel Hilbert space. By designing structured operator-valued kernels, our approach enforces coherence directly within the hypothesis space, ensuring that all predictions satisfy hierarchical constraints by construction. We further propose tailored kernel constructions for hierarchical data and derive excess risk bounds that characterize generalization performance. Empirical results on synthetic and real-world datasets demonstrate the relevance of the proposed method.

Abstract: Retrieval-augmented time-series forecasting uses the continuations of historical segments similar to the current context as references for a forecaster. Most existing methods build the retrieval memory once from the training segment, leaving observations revealed after deployment unavailable as references, and generally do not calibrate how much the retrieved information should influence a frozen forecaster. We identify two key determinants of retrieval utility for a frozen forecaster: whether the history still reflects the current state, and whether the correction it induces aligns with the forecaster's residual errors, an alignment that can shift between validation and deployment when the memory becomes stale. We propose FreshCast, a plug-in retrieval framework that keeps the forecaster frozen, continuously updates a non-parametric memory with new observations, forms a memory forecast through relational kernel regression, and calibrates its weight in closed form on the validation segment. Under a simplified generative model, we characterize the optimal combination gain through the second-order relation between forecaster error and memory correction, and show that a sufficiently long look-back can make periodic memory information redundant. Across seven benchmarks and ten forecasting architectures, FreshCast reduces average MSE for every evaluated forecaster and input length, by 14.6% and 5.6% at input lengths 96 and 720, and achieves lower MSE than the evaluated retrieval-augmented and online baselines in their comparison settings. Ablations show that freezing the memory at the end of training removes most of the gain, identifying post-training observations as a primary source of improvement. For a frozen forecaster, useful historical references must remain timely and provide information that helps correct its remaining errors.

Abstract: Forecasters often know an event is imminent but not the shape, size, or timing of its effect. We introduce Event Signature Transfer (EST), a training-free, model-agnostic operator that turns a completed past event into an explicit forecast scenario. EST removes a source event's own trend and seasonality, then scales and retimes the remaining event signature onto a native forecast, preserving the forecast's linked structure and reducing to it exactly at zero strength. Because it reads only output quantiles, EST applies to any quantile forecaster, with no training, no model internals, at transfer time. Across twelve real episodes and ten synthetic scenarios on Chronos-2, TimesFM-2.5 and Toto-2.0, manually configured EST reduces real-episode WQL by 21.7-90\% in-sample. On Chronos-2, it leads eleven of twelve matched comparisons against covariate conditioning, activation editing and raw replay. The operator builds a scenario; it does not estimate its likelihood.