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. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

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. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

Abstract
When never produced as much data as today, and tomorrow will probably produce even more data. The increase is due not only to the larger number of data sources, but also because the source can continuously produce more recent data. The discovery of temporal patterns in continuously generated data is the main goal in many forecasting tasks, such as the average value of a currency or the average temperature in a city, in the next day. In these tasks, it is assumed that the time difference between two consecutive values produced by the same source is constant, and the sequence of values form a time series. The importance, and the very large number, of time series forecasting tasks make them one of the most popular data analysis application, which has been dealt with by a large number of different methods. Despite its popularity, there is a dearth of research aimed at comprehending the conditions under which these methods present high or poor forecasting performances. Empirical studies, although common, are challenged by the limited availability of time series datasets, restricting the extraction of reliable insights. To address this limitation, we present tsMorph, a tool for generating semi-synthetic time series through dataset morphing. tsMorph works by creating a sequence of datasets from two original datasets. The characteristics of the generated datasets progressively depart from those of one of the datasets and a convergence toward the attributes of the other dataset. This method provides a valuable alternative for obtaining substantial datasets. In this paper, we show the benefits of tsMorph by assessing the predictive performance of the Long Short-Term Memory Network and DeepAR forecasting algorithms. The time series used for the experiments come from the NN5 Competition. The experimental results provide important insights. Notably, the performances of the two algorithms improve proportionally with the frequency of the time series. These experiments confirm that tsMorph can be an effective tool for better understanding the behaviour of forecasting algorithms, delivering a pathway to overcoming the limitations posed by empirical studies and enabling more extensive and reliable experiments. Furthermore, tsMorph can promote Responsible Artificial Intelligence by emphasising characteristics of time series where forecasting algorithms may not perform well, thereby highlighting potential limitations. © 2024 Copyright for this paper by its authors.

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