We propose a novel adaptive Mixture-of-Experts (MoE) framework for time series forecasting that enhances expert specialization by incorporating expert-specific loss information directly into the training process. Notably, the overall objective comprises the base forecasting loss and expert-specific losses, allowing expert-level prediction errors to jointly shape training alongside the global forecasting loss. This framework is further combined with a partial online learning strategy, enabling incremental updates of both the gating mechanism and expert parameters. This approach significantly reduces computational cost by eliminating the need for repeated full model retraining. By integrating expert-level loss awareness with efficient online optimization, the proposed method achieves improved learning efficiency while maintaining strong predictive performance. Empirical results across economic, tourism, and energy datasets with varying frequencies demonstrate that the proposed approach generally outperforms both statistical methods and state-of-the-art neural network models, such as Transformers and WaveNet, in forecasting accuracy and computational efficiency. Furthermore, ablation studies confirm the effectiveness of the expert-specific loss integration strategy, highlighting its contribution to enhancing predictive performance.

We study adaptive pooling under predictive heterogeneity in high-dimensional multivariate time series forecasting, where global models improve statistical efficiency but may fail to capture heterogeneous predictive structure, while naive specialization can induce negative transfer. We formulate adaptive pooling as a statistical decision problem and propose a validation-driven framework that determines when and how specialization should be applied. Rather than grouping series based on representation similarity, we define partitions through out-of-sample predictive performance, thereby aligning data organization with predictive risk, defined as expected out-of-sample loss and approximated via validation error. Cluster assignments are iteratively updated using validation losses for both point (Huber) and probabilistic (pinball) forecasting, improving robustness to heavy-tailed errors and local anomalies. To ensure reliability, we introduce a leakage-free fallback mechanism that reverts to a global model whenever specialization fails to improve validation performance, providing a safeguard against performance degradation under a strict training-validation-test protocol. Experiments on large-scale traffic datasets demonstrate consistent improvements over strong baselines while avoiding degradation when heterogeneity is weak. Overall, the proposed framework provides a principled and practically reliable approach to adaptive pooling in high-dimensional forecasting problems.

We present a novel recurrent neural network architecture designed explicitly for day-ahead electricity price forecasting, aimed at improving short-term decision-making and operational management in energy systems. Our combined forecasting model embeds linear structures, such as expert models and Kalman filters, into recurrent networks, enabling efficient computation and enhanced interpretability. The design leverages the strengths of both linear and non-linear model structures, allowing it to capture all relevant stylised price characteristics in power markets, including calendar and autoregressive effects, as well as influences from load, renewable energy, and related fuel and carbon markets. For empirical testing, we use hourly data from the largest European electricity market spanning 2018 to 2025 in a comprehensive forecasting study, comparing our model against state-of-the-art approaches, particularly high-dimensional linear and neural network models. The proposed model achieves approximately 12% higher accuracy than leading benchmarks. We evaluate the contributions of the interpretable model components and conclude on the impact of combining linear and non-linear structures.

Time series forecasting and anomaly detection are common tasks for practitioners in industries such as retail, manufacturing, advertising and energy. Two unique challenges stand out: (1) efficiently and accurately forecasting time series or detecting anomalies in large volumes automatically; and (2) ensuring interpretability of results to effectively incorporate business insights. We present ARIMA_PLUS, a novel framework to overcome these two challenges by a unique combination of (a) accurate and interpretable time series models and (b) scalable and fully managed system infrastructure. The model has a sequential and modular structure to handle different components of the time series, including holiday effects, seasonality, trend, and anomalies, which enables high interpretability of the results. Novel enhancements are made to each module, and a unified framework is established to address both forecasting and anomaly detection tasks simultaneously. In terms of accuracy, its comprehensive benchmark on the 42 public datasets in the Monash forecasting repository shows superior performance over not only well-established statistical alternatives (such as ETS, ARIMA, TBATS, Prophet) but also newer neural network models (such as DeepAR, N-BEATS, PatchTST, TimeMixer). In terms of infrastructure, it is directly built into the query engine of BigQuery in Google Cloud. It uses a simple SQL interface and automates tedious technicalities such as data cleaning and model selection. It automatically scales with managed cloud computational and storage resources, making it possible to forecast 100 million time series using only 1.5 hours with a throughput of more than 18000 time series per second. In terms of interpretability, we present several case studies to demonstrate time series insights it generates and customizability it offers.

Computational decarbonization aims to reduce carbon emissions in computing and societal systems such as data centers, transportation, and built environments. This requires accurate, fine-grained carbon intensity forecasts, yet existing tools have several key limitations: (i) they require grid-specific electricity mix data, restricting use where such information is unavailable; (ii) they depend on separate grid-specific models that make it challenging to provide global coverage; and (iii) they provide forecasts without uncertainty estimates, limiting reliability for downstream carbon-aware applications. In this paper, we present CarbonX, an open-source tool that leverages Time Series Foundation Models (TSFMs) for a range of decarbonization tasks. CarbonX utilizes the versatility of TSFMs to provide strong performance across multiple tasks, such as carbon intensity forecasting and imputation, and across diverse grids. Using only historical carbon intensity data and a single general model, our tool achieves a zero-shot forecasting Mean Absolute Percentage Error (MAPE) of 15.82% across 214 grids worldwide. Across 13 benchmark grids, CarbonX performance is comparable with the current state-of-the-art, with an average MAPE of 9.59% and tail forecasting MAPE of 16.54%, while also providing prediction intervals with 95% coverage. CarbonX can provide forecasts for up to 21 days with minimal accuracy degradation. Further, when fully fine-tuned, CarbonX outperforms the statistical baselines by 1.2--3.9X on the imputation task. Overall, these results demonstrate that CarbonX can be used easily on any grid with limited data and still deliver strong performance, making it a practical tool for global-scale decarbonization.

Judgmental forecasting employs human opinions to make predictions about future events, rather than exclusively historical data as in quantitative forecasting. When these opinions form an argumentative structure around forecasts, it is useful to study the properties of the forecasts from an argumentative perspective. In this paper, we advocate and formally define a property of argumentative coherence, which, in essence, requires that a forecaster's reasoning is coherent with their forecast. We then conduct three evaluations with our notion of coherence. First, we assess the impact of enforcing coherence on human forecasters as well as on Large Language Model (LLM)-based forecasters, given that they have recently shown to be competitive with human forecasters. In both cases, we show that filtering out incoherent predictions improves forecasting accuracy consistently, supporting the practical value of coherence in both human and LLM-based forecasting. Then, via crowd-sourced user experiments, we show that, despite its apparent intuitiveness and usefulness, users do not generally align with this coherence property. This points to the need to integrate, within argumentation-based judgmental forecasting, mechanisms to filter out incoherent opinions before obtaining group forecasting predictions.

Time series forecasting poses significant challenges in non-stationary environments where underlying patterns evolve over time. In this work, we propose a novel framework that enhances deep neural network (DNN) performance by leveraging specialized model adaptation and selection. Initially, a base DNN is trained offline on historical time series data. A reserved validation subset is then segmented to extract and cluster the most dominant patterns within the series, thereby identifying distinct regimes. For each identified cluster, the base DNN is fine-tuned to produce a specialized version that captures unique pattern characteristics. At inference, the most recent input is matched against the cluster centroids, and the corresponding fine-tuned version is deployed based on the closest similarity measure. Additionally, our approach integrates a concept drift detection mechanism to identify and adapt to emerging patterns caused by non-stationary behavior. The proposed framework is generalizable across various DNN architectures and has demonstrated significant performance gains on both traditional DNNs and recent advanced architectures implemented in the GluonTS library.

Time series forecasting underpins vital decision-making across various sectors, yet raw predictions from sophisticated models often harbor systematic errors and biases. We examine the Forecast-Then-Optimize (FTO) framework, pioneering its systematic synopsis. Unlike conventional Predict-Then-Optimize (PTO) methods, FTO explicitly refines forecasts through optimization techniques such as ensemble methods, meta-learners, and uncertainty adjustments. Furthermore, deep learning and large language models have established superiority over traditional parametric forecasting models for most enterprise applications. This paper surveys significant advancements from 2016 to 2025, analyzing mainstream deep learning FTO architectures. Focusing on real-world applications in operations management, we demonstrate FTO's crucial role in enhancing predictive accuracy, robustness, and decision efficacy. Our study establishes foundational guidelines for future forecasting methodologies, bridging theory and operational practicality.

Time series forecasting has important applications in financial analysis, weather forecasting, and traffic management. However, existing deep learning models are limited in processing non-stationary time series data because they cannot effectively capture the statistical characteristics that change over time. To address this problem, this paper proposes a new framework, AEFIN, which enhances the information sharing ability between stable and unstable components by introducing a cross-attention mechanism, and combines Fourier analysis networks with MLP to deeply explore the seasonal patterns and trend characteristics in unstable components. In addition, we design a new loss function that combines time-domain stability constraints, time-domain instability constraints, and frequency-domain stability constraints to improve the accuracy and robustness of forecasting. Experimental results show that AEFIN outperforms the most common models in terms of mean square error and mean absolute error, especially under non-stationary data conditions, and shows excellent forecasting capabilities. This paper provides an innovative solution for the modeling and forecasting of non-stationary time series data, and contributes to the research of deep learning for complex time series.

Accurate evaluation of forecasting models is essential for ensuring reliable predictions. Current practices for evaluating and comparing forecasting models focus on summarising performance into a single score, using metrics such as SMAPE. While convenient, averaging performance over all samples dilutes relevant information about model behavior under varying conditions. This limitation is especially problematic for time series forecasting, where multiple layers of averaging--across time steps, horizons, and multiple time series in a dataset--can mask relevant performance variations. We address this limitation by proposing ModelRadar, a framework for evaluating univariate time series forecasting models across multiple aspects, such as stationarity, presence of anomalies, or forecasting horizons. We demonstrate the advantages of this framework by comparing 24 forecasting methods, including classical approaches and different machine learning algorithms. NHITS, a state-of-the-art neural network architecture, performs best overall but its superiority varies with forecasting conditions. For instance, concerning the forecasting horizon, we found that NHITS (and also other neural networks) only outperforms classical approaches for multi-step ahead forecasting. Another relevant insight is that classical approaches such as ETS or Theta are notably more robust in the presence of anomalies. These and other findings highlight the importance of aspect-based model evaluation for both practitioners and researchers. ModelRadar is available as a Python package.