## 1 Introduction
to forecast the energy consumption and greenhouse gas (GHG) emission of an Indian pig iron manufacturing organization, and two best fitted ARIMA models are determined respectively [24]. The GARCH model is initially used to forecast the Chicago Board Options Exchange (CBOE) volatility index (VIX) by [PERSON] et al. [25]. With the fast development of artificial intelligence (AI) techniques, artificial neural network (ANN) and machine learning (ML) are gaining increasing focus on forecasting time series data, aiming to overcome the limitations of traditional statistic methods; for instance, they are unable to easily capture nonlinear patterns. [PERSON] et al. [26] propose the back-propagation neural network (BPNN), integrating with design of experiment (DOE) and the Taguchi method, to further optimize the prediction accuracy. According to [PERSON] and [PERSON] [27], a multiple support vector machine (SVM) is presented to study the forecasting of the mid-term electricity market clearing price (MCP). In addition, the application of optimization algorithms [28; 29; 30; 31; 32; 33; 34], such as particle swarm optimization (PSO), artificial bee colony (ABC), fruit fly optimization algorithm (FOA), ant colony optimization (ACO) and differential evolution (DE), has improved the forecasting performance and slowed processing speed of the AI techniques. However, price time series in the real world rarely appears in a linear or nonlinear pattern solely, but usually covers both patterns, so that hybrid models emerge, combining several single models systematically [35], which can simultaneously handle linear and nonlinear patterns [21]. A hybrid methodology that exploits the unique strength of the ARIMA and the SVM is proposed by [PERSON] and [PERSON] [36] to tackle stock prices forecasting problems, which gains very promising results. Since then, it has not been difficult to find that great research efforts have been made to explore the \"linear and nonlinear\" modelling framework used in time series prediction. For example, [PERSON] and [PERSON] [37] present a novel hybridization of ANN and ARIMA to forecast three well-known data sets, namely the [PERSON]'s sunspot data, the Canadian Iynx data and the British bound/US dollar exchange rate. A hybrid model combining VECM and multi-output support vector regression (VECM-MSVR), which is expert in capturing the linear and nonlinear patterns, is devised to make interval forecasting of agricultural commodity futures prices [21]. Undoubtedly, past literature provides many effective and reasonable models to forecast time series and improve the forecasting performance to some extent. However, these models often cannot thoroughly handle the non-stationarity of random and irregular time series. Thus, based on decomposition techniques such as the wavelet transform (WT) family methods, the empirical mode decomposition (EMD) family approaches, and the variational mode decomposition (VMD) method, a promising concept of \"decomposition and ensemble\" is developed [35] to enhance the forecasting ability of the existing models. For example, four real-world time series are predicted through a novel combination of ARIMA and ANN models based on the discrete wavelet transform (DWT) decomposition technique [38]. [PERSON] et al. [39] build a novel least square support vector machine (LSSVM) optimized by PSO based on simulated annealing (PSOSA) (abbreviated as PSOSA-LSSVM) to forecast wind speed data preprocessed by the wavelet packet transform (WPT). According to [PERSON] et al. [40], two kinds of crude oil spot prices, the West Texas Intermediate (WTI) and the Brent, are predicted by the EMD-based neural network. As for intraday stock prices forecasting, [PERSON] [31] develops a hybrid VMD-PSO-BPNN predictive model that finally shows the superiority over the benchmark model, namely a PSO-BPNN model.