The importance of time series forecasting drives continuous research and the development of new approaches to tackle this problem. Typically, these methods are introduced through empirical studies that frequently claim superior accuracy for the proposed approaches. Nevertheless, concerns are rising about the reliability and generalizability of these results due to limitations in experimental setups. This paper addresses a critical limitation: the number and representativeness of the datasets used. We investigate the impact of dataset selection bias, particularly the practice of cherry-picking datasets, on the performance evaluation of forecasting methods. Through empirical analysis with a diverse set of benchmark datasets, our findings reveal that cherry-picking datasets can significantly distort the perceived performance of methods, often exaggerating their effectiveness. Furthermore, our results demonstrate that by selectively choosing just four datasets - what most studies report - 46% of methods could be deemed best in class, and 77% could rank within the top three. Additionally, recent deep learning-based approaches show high sensitivity to dataset selection, whereas classical methods exhibit greater robustness. Finally, our results indicate that, when empirically validating forecasting algorithms on a subset of the benchmarks, increasing the number of datasets tested from 3 to 6 reduces the risk of incorrectly identifying an algorithm as the best one by approximately 40%. Our study highlights the critical need for comprehensive evaluation frameworks that more accurately reflect real-world scenarios. Adopting such frameworks will ensure the development of robust and reliable forecasting methods.

Significant wave height forecasting is a key problem in ocean data analytics. Predicting the significant wave height is crucial for estimating the energy production from waves. Moreover, the timely prediction of large waves is important to ensure the safety of maritime operations, e.g. passage of vessels. We frame the task of predicting extreme values of significant wave height as an exceedance probability forecasting problem. Accordingly, we aim at estimating the probability that the significant wave height will exceed a predefined threshold. This task is usually solved using a probabilistic binary classification model. Instead, we propose a novel approach based on a forecasting model. The method leverages the forecasts for the upcoming observations to estimate the exceedance probability according to the cumulative distribution function. We carried out experiments using data from a buoy placed in the coast of Halifax, Canada. The results suggest that the proposed methodology is better than state-of-the-art approaches for exceedance probability forecasting.

This paper studies the application of ensembles composed of multi-output models for multi-step ahead forecasting problems. Dynamic ensembles have been commonly used for forecasting. However, these are typically designed for one-step-ahead tasks. On the other hand, the literature regarding the application of dynamic ensembles for multi-step ahead forecasting is scarce. Moreover, it is not clear how the combination rule is applied across the forecasting horizon. We carried out extensive experiments to analyze the application of dynamic ensembles for multi-step forecasting. We resorted to a case study with 3568 time series and an ensemble of 30 multi-output models. We discovered that dynamic ensembles based on arbitrating and windowing present the best performance according to average rank. Moreover, as the horizon increases, most approaches struggle to outperform a static ensemble that assigns equal weights to all models. The experiments are publicly available in a repository.

Machine learning models are becoming increasingly popular in different types of settings. This is mainly caused by their ability to achieve a level of predictive performance that is hard to match by human experts in this new era of big data. With this usage growth comes an increase of the requirements for accountability and understanding of the models' predictions. However, the degree of sophistication of the most successful models (e.g. ensembles, deep learning) is becoming a large obstacle to this endeavour as these models are essentially black boxes. In this paper we describe two general approaches that can be used to provide interpretable descriptions of the expected performance of any black box classification model. These approaches are of high practical relevance as they provide means to uncover and describe in an interpretable way situations where the models are expected to have a performance that deviates significantly from their average behaviour. This may be of critical relevance for applications where costly decisions are driven by the predictions of the models, as it can be used to warn end users against the usage of the models in some specific cases.

The predictive advantage of combining several different predictive models is widely accepted. Particularly in time series forecasting problems, this combination is often dynamic to cope with potential non-stationary sources of variation present in the data. Despite their superior predictive performance, ensemble methods entail two main limitations: high computational costs and lack of transparency. These issues often preclude the deployment of such approaches, in favour of simpler yet more efficient and reliable ones. In this paper, we leverage the idea of model compression to address this problem in time series forecasting tasks. Model compression approaches have been mostly unexplored for forecasting. Their application in time series is challenging due to the evolving nature of the data. Further, while the literature focuses on neural networks, we apply model compression to distinct types of methods. In an extensive set of experiments, we show that compressing dynamic forecasting ensembles into an individual model leads to a comparable predictive performance and a drastic reduction in computational costs. Further, the compressed individual model with best average rank is a rule-based regression model. Thus, model compression also leads to benefits in terms of model interpretability. The experiments carried in this paper are fully reproducible.

Evaluating predictive models is a crucial task in predictive analytics. This process is especially challenging with time series data where the observations show temporal dependencies. Several studies have analysed how different performance estimation methods compare with each other for approximating the true loss incurred by a given forecasting model. However, these studies do not address how the estimators behave for model selection: the ability to select the best solution among a set of alternatives. We address this issue and compare a set of estimation methods for model selection in time series forecasting tasks. We attempt to answer two main questions: (i) how often is the best possible model selected by the estimators; and (ii) what is the performance loss when it does not. We empirically found that the accuracy of the estimators for selecting the best solution is low, and the overall forecasting performance loss associated with the model selection process ranges from 1.2% to 2.3%. We also discovered that some factors, such as the sample size, are important in the relative performance of the estimators.

Concept drift detection is a crucial task in data stream evolving environments. Most of state of the art approaches designed to tackle this problem monitor the loss of predictive models. However, this approach falls short in many real-world scenarios, where the true labels are not readily available to compute the loss. In this context, there is increasing attention to approaches that perform concept drift detection in an unsupervised manner, i.e., without access to the true labels. We propose a novel approach to unsupervised concept drift detection based on a student-teacher learning paradigm. Essentially, we create an auxiliary model (student) to mimic the behaviour of the primary model (teacher). At run-time, our approach is to use the teacher for predicting new instances and monitoring the mimicking loss of the student for concept drift detection. In a set of experiments using 19 data streams, we show that the proposed approach can detect concept drift and present a competitive behaviour relative to the state of the art approaches.

The early detection of anomalous events in time series data is essential in many domains of application. In this paper we deal with critical health events, which represent a significant cause of mortality in intensive care units of hospitals. The timely prediction of these events is crucial for mitigating their consequences and improving healthcare. One of the most common approaches to tackle early anomaly detection problems is standard classification methods. In this paper we propose a novel method that uses a layered learning architecture to address these tasks. One key contribution of our work is the idea of pre-conditional events, which denote arbitrary but computable relaxed versions of the event of interest. We leverage this idea to break the original problem into two hierarchical layers, which we hypothesize are easier to solve. The results suggest that the proposed approach leads to a better performance relative to state of the art approaches for critical health episode prediction.

Time series forecasting is one of the most active research topics. Machine learning methods have been increasingly adopted to solve these predictive tasks. However, in a recent work, evidence was shown that these approaches systematically present a lower predictive performance relative to simple statistical methods. In this work, we counter these results. We show that these are only valid under an extremely low sample size. Using a learning curve method, our results suggest that machine learning methods improve their relative predictive performance as the sample size grows.

Performance estimation aims at estimating the loss that a predictive model will incur on unseen data. These procedures are part of the pipeline in every machine learning project and are used for assessing the overall generalisation ability of predictive models. In this paper we address the application of these methods to time series forecasting tasks. For independent and identically distributed data the most common approach is cross-validation. However, the dependency among observations in time series raises some caveats about the most appropriate way to estimate performance in this type of data and currently there is no settled way to do so. We compare different variants of cross-validation and of out-of-sample approaches using two case studies: One with 62 real-world time series and another with three synthetic time series. Results show noticeable differences in the performance estimation methods in the two scenarios. In particular, empirical experiments suggest that cross-validation approaches can be applied to stationary time series. However, in real-world scenarios, when different sources of non-stationary variation are at play, the most accurate estimates are produced by out-of-sample methods that preserve the temporal order of observations.