Abstract
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. We hypothesize that averaging performance over all samples dilutes relevant information about the relative performance of models. Particularly, conditions in which this relative performance is different than the overall accuracy. We address this limitation by proposing a novel framework for evaluating univariate time series forecasting models from multiple perspectives, such as one-step ahead forecasting versus multi-step ahead forecasting. We show the advantages of this framework by comparing a state-of-the-art deep learning approach with classical forecasting techniques. While classical methods (e.g. ARIMA) are long-standing approaches to forecasting, deep neural networks (e.g. NHITS) have recently shown state-of-the-art forecasting performance in benchmark datasets. We conducted extensive experiments that show NHITS generally performs best, but its superiority varies with forecasting conditions. For instance, concerning the forecasting horizon, NHITS only outperforms classical approaches for multi-step ahead forecasting. Another relevant insight is that, when dealing with anomalies, NHITS is outperformed by methods such as Theta. These findings highlight the importance of evaluating forecasts from multiple dimensions.

Abstract
Deep learning approaches are increasingly used to tackle forecasting tasks but require substantial training data. When samples are limited, synthetic data generation techniques can effectively augment datasets to improve model performance. Data augmentation is typically applied offline before training a model. However, when training with mini-batches, some batches may contain a disproportionate number of synthetic samples that do not align well with the original data characteristics. This work introduces an online data augmentation framework that generates synthetic samples during the training of neural networks. By creating synthetic samples for each batch alongside their original counterparts, we maintain a balanced representation between real and synthetic data throughout the training process. This approach fits naturally with the iterative nature of neural network training and eliminates the need to store large augmented datasets. We validated the proposed framework using 3797 time series from 6 benchmark datasets, three neural architectures, and seven synthetic data generation techniques. The experiments suggest that online data augmentation leads to better forecasting performance compared to offline data augmentation or no augmentation approaches. The framework and experiments are publicly available. © 2025 Elsevier B.V., All rights reserved.

Abstract

Abstract
Most forecasting methods use recent past observations (lags) to model the future values of univariate time series. Selecting an adequate number of lags is important for training accurate forecasting models. Several approaches and heuristics have been devised to solve this task. However, there is no consensus about what the best approach is. Besides, lag selection procedures have been developed based on local models and classical forecasting techniques such as ARIMA. We bridge this gap in the literature by carrying out an extensive empirical analysis of different lag selection methods. We focus on deep learning methods trained in a global approach, i.e., on datasets comprising multiple univariate time series. Specifically, we use NHITS, a recently proposed architecture that has shown competitive forecasting performance. The experiments were carried out using three benchmark databases that contain a total of 2411 univariate time series. The results indicate that the lag size is a relevant parameter for accurate forecasts. In particular, excessively small or excessively large lag sizes have a considerable negative impact on forecasting performance. Cross-validation approaches show the best performance for lag selection, but this performance is comparable with simple heuristics.

Abstract
As machine learning technologies are increasingly adopted, the demand for responsible AI practices to ensure transparency and accountability grows. To better understand the decision-making processes of machine learning models, GASTeN was developed to generate realistic yet ambiguous synthetic data near a classifier's decision boundary. However, the results were inconsistent, with few images in the low-confidence region and noise. Therefore, we propose a new GASTeN version with a modified architecture and a novel loss function. This new loss function incorporates a multi-objective measure with a Gaussian loss centered on the classifier probability, targeting the decision boundary. Our study found that while the original GASTeN architecture yields the highest Frechet Inception Distance (FID) scores, the updated version achieves lower Average Confusion Distance (ACD) values and consistent performance across low-confidence regions. Both architectures produce realistic and ambiguous images, but the updated one is more reliable, with no instances of GAN mode collapse. Additionally, the introduction of the Gaussian loss enhanced this architecture by allowing for adjustable tolerance in image generation around the decision boundary.

Abstract
DeepAR is a popular probabilistic time series forecasting algorithm. According to the authors, DeepAR is particularly suitable to build global models using hundreds of related time series. For this reason, it is a common expectation that DeepAR obtains poor results in univariate forecasting [10]. However, there are no empirical studies that clearly support this. Here, we compare the performance of DeepAR with standard forecasting models to assess its performance regarding 1 step-ahead forecasts. We use 100 time series from the M4 competition to compare univariate DeepAR with univariate LSTM and SARIMAX models, both for point and quantile forecasts. Results show that DeepAR obtains good results, which contradicts common perception.