# Time Series Prediction Based on Adaptive Weight Online Sequential Extreme Learning Machine
## 1 Introduction  
Time series prediction technology has already been studied over the past few decades, and a large amount of applications have been reported in a wide range of fields, such as weather forecasting [1], stock market prediction [2], communication signal processing [3], sales forecasting [4], and so on. On account of the frequent applications of time series predictions, plenty of predicting methods have been developed. [PERSON] and [PERSON] gave an overview of various predicting methods and indicated the future directions for time series prediction problems [5]. In particular, the classical statistical linear method, an autoregressive integrated moving average model (ARIMA) based modeling method, is still widely adopted and the complete methodology is able to be found in [PERSON]'s and [PERSON]'s remarkable contribution [6]. However, the predicting accuracy of classical statistical methods suffer from the nonlinearity and complexity of many real time series. For this reason, some computational intelligence methods which may outperform classical statistical methods in many complex nonlinear problems have emerged [7; 8]. Artificial neural network (ANN) methods have attracted extensive attention in the time series prediction field [9]. ANNs are universal nonlinear regression techniques, and are able to be applied into time series prediction conveniently [10]. Furthermore, compared with classical methods, the assumptions for prediction can be relaxed by ANNs, such as Gaussian distribution of noise and the linearity of the model. In contrast to the fact that the model hyperparameters of the ARIMA model is required to be fine-tuned for good prediction, this complication is able to be avoided by ANNs [11]. The hyperparameters of the ARIMA model are quite often adjusted according to domain knowledge, while the ANNs model usually can obtain competitive results without any domain knowledge [12]. For some situations where intensive human adjustment is not affordable, ANNs and other computational intelligence methods are usually better than classical statistical methods. [PERSON] investigated neural network models for forecasting the Indian stock market index [13]. [PERSON] discussed integrating ANN and support vector machine (SVM) methods for long-term prediction, and the stability and accuracy are improved [14]. Nevertheless, since the neural networks used by [PERSON] and [PERSON] are obtained in an iterative way by means of gradient-based algorithms, the diagnosis systems suffer from time-consuming problems. Extreme learning machine (ELM) is a high-efficiency learning algorithm for single-hidden layer feedforward neural network (SLFN), and it has been proven to have classification capacity and universal approximation capacity [15]. In addition, [PERSON] has shown that the hidden-layer parameters can be randomly assigned, and then the output weight is able to be computed analytically [16]. It has been verified that ELM costs much less training time and has better or similar generalization performance than SVM and traditional neural networks [17]. [PERSON] presented the use of wavelet transform and adaptive ELM to forecast outlier occurrence in stock market time series [18]. [PERSON] presented an optimized ELM for predicting financial time series [19]. The ELM based prediction methods have high accuracy and fast learning speed in off-line cases, but they are not suitable for online applications. [PERSON] et al. proposed OS-ELM by incorporating a sequential learning algorithm with ELM [20]. Compared with conventional online training methods, OS-ELM tends to have a faster training speed and better generalization performance. However, in lots of real-world online applications, the confidence coefficient of a sequential data chunk may be disturbed by measurement noise and external disturbance. If the data chunk with low confidence coefficient is employed in the learning process in a normal way, the accuracy of the trained network is likely to be reduced.