A Decomposition-based State Space Model for Multivariate Time-Series Forecasting

Multivariate time series (MTS) forecasting is crucial for decision-making in domains such as weather, energy, and finance. It remains challenging because real-world sequences intertwine slow trends, multi-rate seasonalities, and irregular residuals. Existing methods often rely on rigid, hand-crafted decompositions or generic end-to-end architectures that entangle components and underuse structure shared across variables. To address these limitations, we propose DecompSSM, an end-to-end decomposition framework using three parallel deep state space model branches to capture trend, seasonal, and residual components. The model features adaptive temporal scales via an input-dependent predictor, a refinement module for shared cross-variable context, and an auxiliary loss that enforces reconstruction and orthogonality. Across standard benchmarks (ECL, Weather, ETTm2, and PEMS04), DecompSSM outperformed strong baselines, indicating the effectiveness of combining component-wise deep state space models and global context refinement.

SEDformer: Event-Synchronous Spiking Transformers for Irregular Telemetry Time Series Forecasting

Telemetry streams from large-scale Internet-connected systems (e.g., IoT deployments and online platforms) naturally form an irregular multivariate time series (IMTS) whose accurate forecasting is operationally vital. A closer examination reveals a defining Sparsity-Event Duality (SED) property of IMTS, i.e., long stretches with sparse or no observations are punctuated by short, dense bursts where most semantic events (observations) occur. However, existing Graph- and Transformer-based forecasters ignore SED: pre-alignment to uniform grids with heavy padding violates sparsity by inflating sequences and forcing computation at non-informative steps, while relational recasting weakens event semantics by disrupting local temporal continuity. These limitations motivate a more faithful and natural modeling paradigm for IMTS that aligns with its SED property. We find that Spiking Neural Networks meet this requirement, as they communicate via sparse binary spikes and update in an event-driven manner, aligning naturally with the SED nature of IMTS. Therefore, we present SEDformer, an SED-enhanced Spiking Transformer for telemetry IMTS forecasting that couples: (1) a SED-based Spike Encoder converts raw observations into event synchronous spikes using an Event-Aligned LIF neuron, (2) an Event-Preserving Temporal Downsampling module compresses long gaps while retaining salient firings and (3) a stack of SED-based Spike Transformer blocks enable intra-series dependency modeling with a membrane-based linear attention driven by EA-LIF spiking features. Experiments on public telemetry IMTS datasets show that SEDformer attains state-of-the-art forecasting accuracy while reducing energy and memory usage, providing a natural and efficient path for modeling IMTS.

Bridging Time and Frequency: A Joint Modeling Framework for Irregular Multivariate Time Series Forecasting

Irregular multivariate time series forecasting (IMTSF) is challenging due to non-uniform sampling and variable asynchronicity. These irregularities violate the equidistant assumptions of standard models, hindering local temporal modeling and rendering classical frequency-domain methods ineffective for capturing global periodic structures. To address this challenge, we propose TFMixer, a joint time-frequency modeling framework for IMTS forecasting. Specifically, TFMixer incorporates a Global Frequency Module that employs a learnable Non-Uniform Discrete Fourier Transform (NUDFT) to directly extract spectral representations from irregular timestamps. In parallel, the Local Time Module introduces a query-based patch mixing mechanism to adaptively aggregate informative temporal patches and alleviate information density imbalance. Finally, TFMixer fuses the time-domain and frequency-domain representations to generate forecasts and further leverages inverse NUDFT for explicit seasonal extrapolation. Extensive experiments on real-world datasets demonstrate the state--of-the-art performance of TFMixer.

Diff-MN: Diffusion Parameterized MoE-NCDE for Continuous Time Series Generation with Irregular Observations

Time series generation (TSG) is widely used across domains, yet most existing methods assume regular sampling and fixed output resolutions. These assumptions are often violated in practice, where observations are irregular and sparse, while downstream applications require continuous and high-resolution TS. Although Neural Controlled Differential Equation (NCDE) is promising for modeling irregular TS, it is constrained by a single dynamics function, tightly coupled optimization, and limited ability to adapt learned dynamics to newly generated samples from the generative model. We propose Diff-MN, a continuous TSG framework that enhances NCDE with a Mixture-of-Experts (MoE) dynamics function and a decoupled architectural design for dynamics-focused training. To further enable NCDE to generalize to newly generated samples, Diff-MN employs a diffusion model to parameterize the NCDE temporal dynamics parameters (MoE weights), i.e., jointly learn the distribution of TS data and MoE weights. This design allows sample-specific NCDE parameters to be generated for continuous TS generation. Experiments on ten public and synthetic datasets demonstrate that Diff-MN consistently outperforms strong baselines on both irregular-to-regular and irregular-to-continuous TSG tasks. The code is available at the link https://github.com/microsoft/TimeCraft/tree/main/Diff-MN.

Spatio-Temporal Transformers for Long-Term NDVI Forecasting

Long-term satellite image time series (SITS) analysis in heterogeneous landscapes faces significant challenges, particularly in Mediterranean regions where complex spatial patterns, seasonal variations, and multi-decade environmental changes interact across different scales. This paper presents the Spatio-Temporal Transformer for Long Term Forecasting (STT-LTF ), an extended framework that advances beyond purely temporal analysis to integrate spatial context modeling with temporal sequence prediction. STT-LTF processes multi-scale spatial patches alongside temporal sequences (up to 20 years) through a unified transformer architecture, capturing both local neighborhood relationships and regional climate influences. The framework employs comprehensive self-supervised learning with spatial masking, temporal masking, and horizon sampling strategies, enabling robust model training from 40 years of unlabeled Landsat imagery. Unlike autoregressive approaches, STT-LTF directly predicts arbitrary future time points without error accumulation, incorporating spatial patch embeddings, cyclical temporal encoding, and geographic coordinates to learn complex dependencies across heterogeneous Mediterranean ecosystems. Experimental evaluation on Landsat data (1984-2024) demonstrates that STT-LTF achieves a Mean Absolute Error (MAE) of 0.0328 and R^2 of 0.8412 for next-year predictions, outperforming traditional statistical methods, CNN-based approaches, LSTM networks, and standard transformers. The framework's ability to handle irregular temporal sampling and variable prediction horizons makes it particularly suitable for analysis of heterogeneous landscapes experiencing rapid ecological transitions.

Deep Learning Pose Estimation for Multi-Label Recognition of Combined Hyperkinetic Movement Disorders

Hyperkinetic movement disorders (HMDs) such as dystonia, tremor, chorea, myoclonus, and tics are disabling motor manifestations across childhood and adulthood. Their fluctuating, intermittent, and frequently co-occurring expressions hinder clinical recognition and longitudinal monitoring, which remain largely subjective and vulnerable to inter-rater variability. Objective and scalable methods to distinguish overlapping HMD phenotypes from routine clinical videos are still lacking. Here, we developed a pose-based machine-learning framework that converts standard outpatient videos into anatomically meaningful keypoint time series and computes kinematic descriptors spanning statistical, temporal, spectral, and higher-order irregularity-complexity features.

Rethinking Large Language Models For Irregular Time Series Classification In Critical Care

Time series data from the Intensive Care Unit (ICU) provides critical information for patient monitoring. While recent advancements in applying Large Language Models (LLMs) to time series modeling (TSM) have shown great promise, their effectiveness on the irregular ICU data, characterized by particularly high rates of missing values, remains largely unexplored. This work investigates two key components underlying the success of LLMs for TSM: the time series encoder and the multimodal alignment strategy. To this end, we establish a systematic testbed to evaluate their impact across various state-of-the-art LLM-based methods on benchmark ICU datasets against strong supervised and self-supervised baselines. Results reveal that the encoder design is more critical than the alignment strategy. Encoders that explicitly model irregularity achieve substantial performance gains, yielding an average AUPRC increase of $12.8\%$ over the vanilla Transformer. While less impactful, the alignment strategy is also noteworthy, with the best-performing semantically rich, fusion-based strategy achieving a modest $2.9\%$ improvement over cross-attention. However, LLM-based methods require at least 10$\times$ longer training than the best-performing irregular supervised models, while delivering only comparable performance. They also underperform in data-scarce few-shot learning settings. These findings highlight both the promise and current limitations of LLMs for irregular ICU time series. The code is available at https://github.com/mHealthUnimelb/LLMTS.

MN-TSG:Continuous Time Series Generation with Irregular Observations

Time series generation (TSG) plays a critical role in a wide range of domains, such as healthcare. However, most existing methods assume regularly sampled observations and fixed output resolutions, which are often misaligned with real-world scenarios where data are irregularly sampled and sparsely observed. This mismatch is particularly problematic in applications such as clinical monitoring, where irregular measurements must support downstream tasks requiring continuous and high-resolution time series. Neural Controlled Differential Equations (NCDEs) have shown strong potential for modeling irregular time series, yet they still face challenges in capturing complex dynamic temporal patterns and supporting continuous TSG. To address these limitations, we propose MN-TSG, a novel framework that explores Mixture-of-Experts (MoE)-based NCDEs and integrates them with existing TSG models for irregular and continuous generation tasks. The core of MN-TSG lies in a MoE-NCDE architecture with dynamically parameterized expert functions and a decoupled design that facilitates more effective optimization of MoE dynamics. Furthermore, we leverage existing TSG models to learn the joint distribution over the mixture of experts and the generated time series. This enables the framework not only to generate new samples, but also to produce appropriate expert configurations tailored to each sample, thereby supporting refined continuous TSG. Extensive experiments on ten public and synthetic datasets demonstrate the effectiveness of MN-TSG, consistently outperforming strong TSG baselines on both irregular-to-regular and irregular-to-continuous generation tasks.

Data-driven Lake Water Quality Forecasting for Time Series with Missing Data using Machine Learning

Volunteer-led lake monitoring yields irregular, seasonal time series with many gaps arising from ice cover, weather-related access constraints, and occasional human errors, complicating forecasting and early warning of harmful algal blooms. We study Secchi Disk Depth (SDD) forecasting on a 30-lake, data-rich subset drawn from three decades of in situ records collected across Maine lakes. Missingness is handled via Multiple Imputation by Chained Equations (MICE), and we evaluate performance with a normalized Mean Absolute Error (nMAE) metric for cross-lake comparability. Among six candidates, ridge regression provides the best mean test performance. Using ridge regression, we then quantify the minimal sample size, showing that under a backward, recent-history protocol, the model reaches within 5% of full-history accuracy with approximately 176 training samples per lake on average. We also identify a minimal feature set, where a compact four-feature subset matches the thirteen-feature baseline within the same 5% tolerance. Bringing these results together, we introduce a joint feasibility function that identifies the minimal training history and fewest predictors sufficient to achieve the target of staying within 5% of the complete-history, full-feature baseline. In our study, meeting the 5% accuracy target required about 64 recent samples and just one predictor per lake, highlighting the practicality of targeted monitoring. Hence, our joint feasibility strategy unifies recent-history length and feature choice under a fixed accuracy target, yielding a simple, efficient rule for setting sampling effort and measurement priorities for lake researchers.

Temporal Fusion Nexus: A task-agnostic multi-modal embedding model for clinical narratives and irregular time series in post-kidney transplant care

We introduce Temporal Fusion Nexus (TFN), a multi-modal and task-agnostic embedding model to integrate irregular time series and unstructured clinical narratives. We analysed TFN in post-kidney transplant (KTx) care, with a retrospective cohort of 3382 patients, on three key outcomes: graft loss, graft rejection, and mortality. Compared to state-of-the-art model in post KTx care, TFN achieved higher performance for graft loss (AUC 0.96 vs. 0.94) and graft rejection (AUC 0.84 vs. 0.74). In mortality prediction, TFN yielded an AUC of 0.86. TFN outperformed unimodal baselines (approx 10% AUC improvement over time series only baseline, approx 5% AUC improvement over time series with static patient data). Integrating clinical text improved performance across all tasks. Disentanglement metrics confirmed robust and interpretable latent factors in the embedding space, and SHAP-based attributions confirmed alignment with clinical reasoning. TFN has potential application in clinical tasks beyond KTx, where heterogeneous data sources, irregular longitudinal data, and rich narrative documentation are available.