PRISM: A hierarchical multiscale approach for time series forecasting

Forecasting is critical in areas such as finance, biology, and healthcare. Despite the progress in the field, making accurate forecasts remains challenging because real-world time series contain both global trends, local fine-grained structure, and features on multiple scales in between. Here, we present a new forecasting method, PRISM (Partitioned Representation for Iterative Sequence Modeling), that addresses this challenge through a learnable tree-based partitioning of the signal. At the root of the tree, a global representation captures coarse trends in the signal, while recursive splits reveal increasingly localized views of the signal. At each level of the tree, data are projected onto a time-frequency basis (e.g., wavelets or exponential moving averages) to extract scale-specific features, which are then aggregated across the hierarchy. This design allows the model to jointly capture global structure and local dynamics of the signal, enabling accurate forecasting. Experiments across benchmark datasets show that our method outperforms state-of-the-art methods for forecasting. Overall, these results demonstrate that our hierarchical approach provides a lightweight and flexible framework for forecasting multivariate time series. The code is available at https://github.com/nerdslab/prism.

Causality-Inspired Safe Residual Correction for Multivariate Time Series

While modern multivariate forecasters such as Transformers and GNNs achieve strong benchmark performance, they often suffer from systematic errors at specific variables or horizons and, critically, lack guarantees against performance degradation in deployment. Existing post-hoc residual correction methods attempt to fix these errors, but are inherently greedy: although they may improve average accuracy, they can also "help in the wrong way" by overcorrecting reliable predictions and causing local failures in unseen scenarios. To address this critical "safety gap," we propose CRC (Causality-inspired Safe Residual Correction), a plug-and-play framework explicitly designed to ensure non-degradation. CRC follows a divide-and-conquer philosophy: it employs a causality-inspired encoder to expose direction-aware structure by decoupling self- and cross-variable dynamics, and a hybrid corrector to model residual errors. Crucially, the correction process is governed by a strict four-fold safety mechanism that prevents harmful updates. Experiments across multiple datasets and forecasting backbones show that CRC consistently improves accuracy, while an in-depth ablation study confirms that its core safety mechanisms ensure exceptionally high non-degradation rates (NDR), making CRC a correction framework suited for safe and reliable deployment.

DecoKAN: Interpretable Decomposition for Forecasting Cryptocurrency Market Dynamics

Accurate and interpretable forecasting of multivariate time series is crucial for understanding the complex dynamics of cryptocurrency markets in digital asset systems. Advanced deep learning methodologies, particularly Transformer-based and MLP-based architectures, have achieved competitive predictive performance in cryptocurrency forecasting tasks. However, cryptocurrency data is inherently composed of long-term socio-economic trends and local high-frequency speculative oscillations. Existing deep learning-based 'black-box' models fail to effectively decouple these composite dynamics or provide the interpretability needed for trustworthy financial decision-making. To overcome these limitations, we propose DecoKAN, an interpretable forecasting framework that integrates multi-level Discrete Wavelet Transform (DWT) for decoupling and hierarchical signal decomposition with Kolmogorov-Arnold Network (KAN) mixers for transparent and interpretable nonlinear modeling. The DWT component decomposes complex cryptocurrency time series into distinct frequency components, enabling frequency-specific analysis, while KAN mixers provide intrinsically interpretable spline-based mappings within each decomposed subseries. Furthermore, interpretability is enhanced through a symbolic analysis pipeline involving sparsification, pruning, and symbolization, which produces concise analytical expressions offering symbolic representations of the learned patterns. Extensive experiments demonstrate that DecoKAN achieves the lowest average Mean Squared Error on all tested real-world cryptocurrency datasets (BTC, ETH, XMR), consistently outperforming a comprehensive suite of competitive state-of-the-art baselines. These results validate DecoKAN's potential to bridge the gap between predictive accuracy and model transparency, advancing trustworthy decision support within complex cryptocurrency markets.

Guardrailed Elasticity Pricing: A Churn-Aware Forecasting Playbook for Subscription Strategy

This paper presents a marketing analytics framework that operationalizes subscription pricing as a dynamic, guardrailed decision system, uniting multivariate demand forecasting, segment-level price elasticity, and churn propensity to optimize revenue, margin, and retention. The approach blends seasonal time-series models with tree-based learners, runs Monte Carlo scenario tests to map risk envelopes, and solves a constrained optimization that enforces business guardrails on customer experience, margin floors, and allowable churn. Validated across heterogeneous SaaS portfolios, the method consistently outperforms static tiers and uniform uplifts by reallocating price moves toward segments with higher willingness-to-pay while protecting price-sensitive cohorts. The system is designed for real-time recalibration via modular APIs and includes model explainability for governance and compliance. Managerially, the framework functions as a strategy playbook that clarifies when to shift from flat to dynamic pricing, how to align pricing with CLV and MRR targets, and how to embed ethical guardrails, enabling durable growth without eroding customer trust.

Adaptive Information Routing for Multimodal Time Series Forecasting

Time series forecasting is a critical task for artificial intelligence with numerous real-world applications. Traditional approaches primarily rely on historical time series data to predict the future values. However, in practical scenarios, this is often insufficient for accurate predictions due to the limited information available. To address this challenge, multimodal time series forecasting methods which incorporate additional data modalities, mainly text data, alongside time series data have been explored. In this work, we introduce the Adaptive Information Routing (AIR) framework, a novel approach for multimodal time series forecasting. Unlike existing methods that treat text data on par with time series data as interchangeable auxiliary features for forecasting, AIR leverages text information to dynamically guide the time series model by controlling how and to what extent multivariate time series information should be combined. We also present a text-refinement pipeline that employs a large language model to convert raw text data into a form suitable for multimodal forecasting, and we introduce a benchmark that facilitates multimodal forecasting experiments based on this pipeline. Experiment results with the real world market data such as crude oil price and exchange rates demonstrate that AIR effectively modulates the behavior of the time series model using textual inputs, significantly enhancing forecasting accuracy in various time series forecasting tasks.

SEED: Spectral Entropy-Guided Evaluation of SpatialTemporal Dependencies for Multivariate Time Series Forecasting

Effective multivariate time series forecasting often benefits from accurately modeling complex inter-variable dependencies. However, existing attention- or graph-based methods face three key issues: (a) strong temporal self-dependencies are often disrupted by irrelevant variables; (b) softmax normalization ignores and reverses negative correlations; (c) variables struggle to perceive their temporal positions. To address these, we propose \textbf{SEED}, a Spectral Entropy-guided Evaluation framework for spatial-temporal Dependency modeling. SEED introduces a Dependency Evaluator, a key innovation that leverages spectral entropy to dynamically provide a preliminary evaluation of the spatial and temporal dependencies of each variable, enabling the model to adaptively balance Channel Independence (CI) and Channel Dependence (CD) strategies. To account for temporal regularities originating from the influence of other variables rather than intrinsic dynamics, we propose Spectral Entropy-based Fuser to further refine the evaluated dependency weights, effectively separating this part. Moreover, to preserve negative correlations, we introduce a Signed Graph Constructor that enables signed edge weights, overcoming the limitations of softmax. Finally, to help variables perceive their temporal positions and thereby construct more comprehensive spatial features, we introduce the Context Spatial Extractor, which leverages local contextual windows to extract spatial features. Extensive experiments on 12 real-world datasets from various application domains demonstrate that SEED achieves state-of-the-art performance, validating its effectiveness and generality.

A lightweight Spatial-Temporal Graph Neural Network for Long-term Time Series Forecasting

We propose Lite-STGNN, a lightweight spatial-temporal graph neural network for long-term multivariate forecasting that integrates decomposition-based temporal modeling with learnable sparse graph structure. The temporal module applies trend-seasonal decomposition, while the spatial module performs message passing with low-rank Top-$K$ adjacency learning and conservative horizon-wise gating, enabling spatial corrections that enhance a strong linear baseline. Lite-STGNN achieves state-of-the-art accuracy on four benchmark datasets for horizons up to 720 steps, while being parameter-efficient and substantially faster to train than transformer-based methods. Ablation studies show that the spatial module yields 4.6% improvement over the temporal baseline, Top-$K$ enhances locality by 3.3%, and learned adjacency matrices reveal domain-specific interaction dynamics. Lite-STGNN thus offers a compact, interpretable, and efficient framework for long-term multivariate time series forecasting.

FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation

Multivariate time series imputation is fundamental in applications such as healthcare, traffic forecasting, and biological modeling, where sensor failures and irregular sampling lead to pervasive missing values. However, existing Transformer- and diffusion-based models lack explicit inductive biases and frequency awareness, limiting their generalization under structured missing patterns and distribution shifts. We propose FADTI, a diffusion-based framework that injects frequency-informed feature modulation via a learnable Fourier Bias Projection (FBP) module and combines it with temporal modeling through self-attention and gated convolution. FBP supports multiple spectral bases, enabling adaptive encoding of both stationary and non-stationary patterns. This design injects frequency-domain inductive bias into the generative imputation process. Experiments on multiple benchmarks, including a newly introduced biological time series dataset, show that FADTI consistently outperforms state-of-the-art methods, particularly under high missing rates. Code is available at https://anonymous.4open.science/r/TimeSeriesImputation-52BF

Pattern-Guided Diffusion Models

Diffusion models have shown promise in forecasting future data from multivariate time series. However, few existing methods account for recurring structures, or patterns, that appear within the data. We present Pattern-Guided Diffusion Models (PGDM), which leverage inherent patterns within temporal data for forecasting future time steps. PGDM first extracts patterns using archetypal analysis and estimates the most likely next pattern in the sequence. By guiding predictions with this pattern estimate, PGDM makes more realistic predictions that fit within the set of known patterns. We additionally introduce a novel uncertainty quantification technique based on archetypal analysis, and we dynamically scale the guidance level based on the pattern estimate uncertainty. We apply our method to two well-motivated forecasting applications, predicting visual field measurements and motion capture frames. On both, we show that pattern guidance improves PGDM's performance (MAE / CRPS) by up to 40.67% / 56.26% and 14.12% / 14.10%, respectively. PGDM also outperforms baselines by up to 65.58% / 84.83% and 93.64% / 92.55%.

Weighted Contrastive Learning for Anomaly-Aware Time-Series Forecasting

Reliable forecasting of multivariate time series under anomalous conditions is crucial in applications such as ATM cash logistics, where sudden demand shifts can disrupt operations. Modern deep forecasters achieve high accuracy on normal data but often fail when distribution shifts occur. We propose Weighted Contrastive Adaptation (WECA), a Weighted contrastive objective that aligns normal and anomaly-augmented representations, preserving anomaly-relevant information while maintaining consistency under benign variations. Evaluations on a nationwide ATM transaction dataset with domain-informed anomaly injection show that WECA improves SMAPE on anomaly-affected data by 6.1 percentage points compared to a normally trained baseline, with negligible degradation on normal data. These results demonstrate that WECA enhances forecasting reliability under anomalies without sacrificing performance during regular operations.