## 2 Background
### A Brief Review of the Literature  
By also extending a recently done literature review by the author and his colleague in [10], it is possible to explain some of the background on time series prediction (mostly on chaotic ones) as follows:  
Considering the technique of artificial neural networks (ANN), [PERSON] et al. and [PERSON] et al. all introduced some prediction-oriented research studies for the related literature [11; 12]. In terms of hybrid approaches, [PERSON] et al. employed a nonlinear local predictor, the feed forward artificial neural network, and fuzzy logic to realize predictions on time series of aperiodic hydrodynamic oscillations [13]. Predicting multivariate chaotic time series is a challenging research issue. At this point, [PERSON] and [PERSON] performed a study using the radial basis function (RBF) to deal with the related research issues [14]. In the literature, some well-known chaotic time series have been used to evaluate different approaches. In a remarkable example, [PERSON] et al. predicted the time series of Mackey-Glass, and the gas furnace (Box-Jenkins), thanks to the iterated extended Kalman filter with the single multiplicative neuron model [15]. In addition, they also performed predictions over EEG time series. Based on the use of single multiplicative neuron (SMN) for the prediction of time series, it is possible to find many alternative studies that have been done so far. For example, [PERSON] et al. used this technique in their study which was published in 2007 [16]. Additionally, [PERSON] and [PERSON] performed a study similar to [14], but they used the SMN-PSO (particle swarm optimization trained SMN) approach to predict the Mackey-Glass, gas furnace (Box-Jenkins), and EEG time series [17]. [PERSON] and [PERSON] benefited from a fuzzy logic (FL)-based approach to deal with the prediction issues about atmospheric visibility in the city of Shanghai, China [18]. Particle swarm optimization (PSO), which is a widely-used swarm intelligence technique, was used by [PERSON] to perform optimization-based time series prediction applications [19]. In another study, [PERSON] et al. used PSO in order to obtain optimum ensemble of Extreme Learning Machines (ELM) for time series prediction [20]. Ant colony optimization (ACO), a combinatorial optimization algorithm that is widely-known in the literature, has become another effective prediction method for chaotic flows. Some examples are shown in [5; 21; 22; 23; 24]. [PERSON] used a model which provides a parameter-free simplified swarm optimization for the training of artificial neural networks (ANN) [25]. In that study, the model was run over different time series, including EEG. In a remarkable study, [PERSON] and [PERSON] employed a Wavelet least square support vector machine (WLSSVM) system to predict hydrological time series [26]. By focusing of the issue of predicting a suspended sediment load (SSL) for the Aji-Chay River (monthly), the authors performed a comparison-based prediction approach which analyzed approaches like ad-hoc the least square support vector machine (LSSVM) and models of artificial neural networks (ANN) together. Regarding the sub-field of machine learning, [PERSON] et al. produced a book chapter to provide a review about recent approaches for predicting the time series via specific machine learning techniques [27]. As it is based on a research study focused on prediction of general time series, this study is different from the alternative ones including only chaotic time series. It is an important background study due to its publishing year and wide scope. The literature also includes some studies in which the authors employed hybrid systems structured via optimization algorithms and SVM to overcome the time series prediction problem. For example, [PERSON] and [PERSON] employed support vector machines (SVM) and the chaotic simulated annealing algorithm (CSAA) to predict time series [28].