## 1 Introduction
[13] proposed a forecasting method based on an integrated genetic algorithm and the ARMA model in order to gain the advantage of both of these tools in the forecasting of data. They used a genetic algorithm to optimize \(AR(p)\) and \(MA(q)\) and find the best ARMA model for the problem. They found that their model had an effective identification for estimating ARMA autoregression and moving averages. However, these authors presented ARIMA parameters with limited possibilities. In addition, they used only one forecasting error rate to judge the forecasting accuracy. [PERSON] et al. [14] maintained that the back-propagation neural network (BPNN) can easily fall into the local minimum point in time series forecasting. They developed a hybrid approach that combines the adaptive differential evolution (ADE) algorithm with the BPNN. This approach was called the ADE-BPNN and was designed to improve the forecasting accuracy of the BPNN. The initial connection weights and thresholds of the BPNN as a single hidden layer are selected by combining the ADE with the BPNN. The ADE is used to search preliminarily for the global optimal connection weights and thresholds of the BPNN. The ADE is adopted to explore the search space and detect potential regions. The model of [PERSON] et al. [14] shows good performance in solving complex optimization problems. However, their model needs to be improved to handle complex application problems and find the best appropriate structure and parameters. [PERSON] et al. [15] utilised the ADE-BPNN to estimate energy consumption. The hybrid model created by these authors incorporates gross domestic product, population, import, and export data as inputs. In this approach, an improved differential evolution with adaptive mutation and crossover is utilised to find appropriate global initial connection weights and thresholds to enhance the forecasting performance of the BPNN. [PERSON] et al. [15] used an adaptive DE (ADE) algorithm to find appropriate initial connection weights and thresholds of a BPNN for obtaining more accurate forecasting. The BPNN was utilised to achieve good-fitting performance and high forecasting precision. A BPNN is a multilayer mapping network that minimizes errors backward while transmitting information. The prediction accuracy of the authors' method is relatively high because an improved ADE with good balance between the search speed and accuracy assists in finding appropriate global initial connection weights and thresholds to enhance the forecasting performance of the BPNN effectively. However, their model needs to be improved for long-term forecasts and processing big data. [PERSON] et al. (2016) proposed a combination model resulting from a new neural networks-based linear ensemble framework (NNsLEF). The proposed framework can merge the advantages of component neural networks and dynamic weight combination approaches to improve the forecasting performance. Four neural network models are applied to impart their superior performance to the combination approach while maintaining their diversity. The framework proposed by [PERSON] et al. (2016) adheres to three primary principles. (a) Four kinds of neural network models, namely the back-propagation neural network, an artificial neural network with a dynamic architecture, the Elman artificial neural network, and the echo state network, are selected as component forecasting models. (b) An input-hidden selection heuristic (IHSH) is designed to determine the input-hidden neuron combination for each component neural network. (c) An in-sample training-validation pair-based neural network weighting (ITVPNNW) mechanism is studied to generate the associated combination weights. The NNsLEF aims to improve the accuracy of time series forecasting and could provide an effective forecast through the mentioned combination model. However, this approach has limitations and its complexity means that there are a low number of relevant application areas with large data samples.