Multivariate time-series forecasting plays a crucial role in many real-world applications.

Time-series forecasting tasks are central to a broad range of application domains, including stock pricepredictions [1,2],servicedemandforecasting [3,4],andmedicalprognoses[5-7].

We introduce a model-agnostic forward diffusion process for time-series forecasting that decomposes signals into spectral components, preserving structured temporal patterns such as seasonality more effectively than standard diffusion. Unlike prior work that modifies the network architecture or diffuses directly in the frequency domain, our proposed method alters only the diffusion process itself, making it compatible with existing diffusion backbones (e.g., DiffWave, TimeGrad, CSDI). By staging noise injection according to component energy, it maintains high signal-to-noise ratios for dominant frequencies throughout the diffusion trajectory, thereby improving the recoverability of long-term patterns. This strategy enables the model to maintain the signal structure for a longer period in the forward process, leading to improved forecast quality. Across standard forecasting benchmarks, we show that applying spectral decomposition strategies, such as the Fourier or Wavelet transform, consistently improves upon diffusion models using the baseline forward process, with negligible computational overhead. The code for this paper is available at https://anonymous.4open.science/r/D-FDP-4A29.

Delivering precise point and distributional forecasts across a spectrum of prediction horizons represents a significant and enduring challenge in the application of time-series forecasting within various industries.Prior research on developing deep learning models for time-series forecasting has often concentrated on isolated aspects, such as long-term point forecasting or short-term probabilistic estimations. This narrow focus may result in skewed methodological choices and hinder the adaptability of these models to uncharted scenarios.While there is a rising trend in developing universal forecasting models, a thorough understanding of their advantages and drawbacks, especially regarding essential forecasting needs like point and distributional forecasts across short and long horizons, is still lacking.In this paper, we present ProbTS, a benchmark tool designed as a unified platform to evaluate these fundamental forecasting needs and to conduct a rigorous comparative analysis of numerous cutting-edge studies from recent years.We dissect the distinctive data characteristics arising from disparate forecasting requirements and elucidate how these characteristics can skew methodological preferences in typical research trajectories, which often fail to fully accommodate essential forecasting needs.Building on this, we examine the latest models for universal time-series forecasting and discover that our analyses of methodological strengths and weaknesses are also applicable to these universal models.Finally, we outline the limitations inherent in current research and underscore several avenues for future exploration.

Spiking neural networks (SNNs) represent a promising approach to developing artificial neural networks that are both energy-efficient and biologically plausible.However, applying SNNs to sequential tasks, such as text classification and time-series forecasting, has been hindered by the challenge of creating an effective and hardware-friendly spike-form positional encoding (PE) strategy.Drawing inspiration from the central pattern generators (CPGs) in the human brain, which produce rhythmic patterned outputs without requiring rhythmic inputs, we propose a novel PE technique for SNNs, termed CPG-PE.We demonstrate that the commonly used sinusoidal PE is mathematically a specific solution to the membrane potential dynamics of a particular CPG.Moreover, extensive experiments across various domains, including time-series forecasting, natural language processing, and image classification, show that SNNs with CPG-PE outperform their conventional counterparts.Additionally, we perform analysis experiments to elucidate the mechanism through which SNNs encode positional information and to explore the function of CPGs in the human brain.This investigation may offer valuable insights into the fundamental principles of neural computation.

Yet, such GNN models pre-dominantly capture only lower order interactions, that is, pairwise relations among nodes, and also largely ignore intrinsic time-conditioned information on the underlying topology of multivariate time series. To address these limitations, we propose a new time-aware GNN architecture which amplifies the power of the recently emerged simplicial neural networks with a time-conditioned topological knowledge representation in a form of zigzag persistence. That is, our new approach, Zigzag Filtration Curve based Supra-Hodge Convolution Networks (ZFC-SHCN) is built upon the two main components: (i) a new highly computationally efficientzigzag persistence curve which allows us to systematically encode time-conditioned topological information, and (ii) a new temporal multiplex graph representation module for learning higher-order network interactions. We discuss theoretical properties of the proposed time-conditioned topological knowledge representation and extensively validate the new time-aware ZFC-SHCN model in conjunction with time series forecasting on a broad range of synthetic and real-world datasets: traffic flows, COVID-19 biosurveillance, Ethereum blockchain, surface air temperature, wind energy, and vector autoregressions. Our experiments demonstrate that the ZFC-SHCN achieves the state-of-the-art performance with lower requirements on computational costs.

Deep learning (DL) models, a specialized class of multilayer neural networks, have become central to time-series forecasting in critical domains such as environmental monitoring and the Internet of Things (IoT). Among these, Bidirectional Long Short-Term Memory (BiLSTM) architectures are particularly effective in capturing complex temporal dependencies. However, the robustness and generalization of such models are highly sensitive to input data characteristics - an aspect that remains underexplored in existing literature. This study presents a systematic empirical analysis of two key data-centric factors: input sequence length and additive noise. To support this investigation, a modular and reproducible forecasting pipeline is developed, incorporating standardized preprocessing, sequence generation, model training, validation, and evaluation. Controlled experiments are conducted on three real-world datasets with varying sampling frequencies to assess BiLSTM performance under different input conditions. The results yield three key findings: (1) longer input sequences significantly increase the risk of overfitting and data leakage, particularly in data-constrained environments; (2) additive noise consistently degrades predictive accuracy across sampling frequencies; and (3) the simultaneous presence of both factors results in the most substantial decline in model stability. While datasets with higher observation frequencies exhibit greater robustness, they remain vulnerable when both input challenges are present. These findings highlight important limitations in current DL-based forecasting pipelines and underscore the need for data-aware design strategies. This work contributes to a deeper understanding of DL model behavior in dynamic time-series environments and provides practical insights for developing more reliable and generalizable forecasting systems.

Time series forecasting in real world environments faces significant challenges non stationarity, multi scale temporal patterns, and distributional shifts that degrade model stability and accuracy. This study propose AdaMamba, a unified forecasting architecture that integrates adaptive normalization, multi scale trend extraction, and contextual sequence modeling to address these challenges. AdaMamba begins with an Adaptive Normalization Block that removes non stationary components through multi scale convolutional trend extraction and channel wise recalibration, enabling consistent detrending and variance stabilization. The normalized sequence is then processed by a Context Encoder that combines patch wise embeddings, positional encoding, and a Mamba enhanced Transformer layer with a mixture of experts feed forward module, allowing efficient modeling of both long range dependencies and local temporal dynamics. A lightweight prediction head generates multi horizon forecasts, and a denormalization mechanism reconstructs outputs by reintegrating local trends to ensure robustness under varying temporal conditions. AdaMamba provides strong representational capacity with modular extensibility, supporting deterministic prediction and compatibility with probabilistic extensions. Its design effectively mitigates covariate shift and enhances predictive reliability across heterogeneous datasets. Experimental evaluations demonstrate that AdaMamba's combination of adaptive normalization and expert augmented contextual modeling yields consistent improvements in stability and accuracy over conventional Transformer based baselines.