**1. Introduction**

Time series forecasting is a highly important and dynamic research domain, which has wide applicability to many diverse scientific fields, ranging from ecological modeling to energy [1],

finance [2,3], tourism [4,5], and electricity load [6,7]. A summary of applications regarding forecasting in various areas can be found in a plethora of review papers published in the relevant literature [8–15]. One of the main challenges in the field of time series forecasting is to obtain reasonable and accurate forecasts of future data from analyzing previous historical data [16]. Following the literature, numerous research studies show that forecasting accuracy is improved when di fferent models are combined, while the resulting model seems to outperform all component models [16]. Thus, the combination of forecasts from di fferent models or algorithms becomes a promising field in the prediction of future data.

Researchers can choose between linear and nonlinear time series forecasting methods, depending on the nature of the model they are working on. Linear methods, like autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) [17] are among the methodologies which have found wide applicability in real-world applications. Traffic [18], energy [19–21], economy [22], tourism [23], and health [24] are some example fields in which the ARIMA forecasting technique was used. Considering though that most real-world problems are characterized by a non-linear behavior, many researchers have investigated the use of non-linear techniques for times series-based forecasting and prediction. In particular, machine learning and other intelligent methods have been chosen to address possible nonlinearities in time series modeling, such as nonlinear ARMA time series models, needing though to tackle the type of nonlinearity that is not usually known. Along with the computing power growth and the evolution of data managemen<sup>t</sup> techniques, there has been a growing interest in the use of advanced artificial intelligence technologies, like artificial neural networks (ANNs) [25] and fuzzy logic systems for forecasting purposes. ANNs and fuzzy logic systems use more sophisticated generic model structures having the ability to incorporate the characteristics of complex data and produce accurate time series models [26], while they also incorporate the advantageous features of nonlinear modeling and data-based learning capabilities. Moreover, unlike traditional time series methods that are not able to adequately capture nonlinear patterns of data, neural networks are usually involved in predicting consumption demand during periods of low or extremely high demand [27]. Among all types of ANN models, the feed-forward network model with backpropagation training procedure (FFN-BP) is one of the most commonly used approaches [28].

The technique of combining the predictions of multiple classifiers to produce a single classifier is referred to as an ensemble [29–32]. Ensemble building has recently attracted much attention among researchers as an e ffective method that improves the performance of the resulting model for performing classification and regression tasks. It has been demonstrated that an ensemble of individual predictors performs better than a single predictor in the average [33,34], thus achieving better prediction accuracy than that of the individual predictors. Two popular methods for creating accurate ensembles are bagging [29] and boosting [35,36]. There are not many research works concerning potency forecasting of a model in advance, as this is often a di fficult task. Trying to avoid the risk of combining models that have poor performance regarding prediction may result in an overall model with deteriorated forecasting accuracy. An ensemble model, however, should rather be formed solely from component models that are rated as adequate, if not good enough, for their forecasting capabilities [37]. Usually, the single neural network (NN) models are combined to create NNs ensembles, to tackle sampling and modeling uncertainties that could probably weaken the forecasting accuracy and robustness of component NN models. Since individual component model could be sensitive under di fferent circumstances, ensembling them results in more powerful outcomes in the context of a decision-making process.
