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Top1. Introduction
Feedforward neural networks have been widely used in prediction of stock index and different areas of research. Stock index prediction depends on the direction of movement of price index. So a financial trader to decide whether to buy or sell depends on the accurate prediction of stock index. The behavior of a stock index is dynamic in nature and non-linear. Rumelhart et al.(1986) suggested Backpropagation algorithm as the first gradient method used for parameter optimization. Hagan and Menhaj (1994) incorporated Marquardt algorithm with backpropagation which was found to be more efficient than conjugate gradient algorithm. Guresen et al.(2011) introduced dynamic artificial neural network and hybrid neural network for forecasting time series data. Huang, Zhu, and Siew (2004) proposed an efficient training algorithm consisting of a single hidden layer feedforward neural network called Extreme Learning Machine (ELM).In comparison with other feedforward network ELM guarantees global optimal solution. Conventional ELM model randomly starts with generated weights and bias. Researchers (Huang, Zhu, and Siew, 2006; Huang, Chen, and Siew, 2006; Huang and Chen, 2007; Huang and Chen, 2008).have proved ELM to be efficient in universal approximation of single layer feedforward network.
Critical analysis of recent literature reveals that ELM is focused on fast learning and is capable of higher generalized performance over traditional time series prediction algorithms. An extensive study on learning efficiency and accuracy of ELM classification and regression is proposed by Huang, Zhou, Ding and Zhang(2012). Lan, Soh, and Huang(2010) performed a two-stage ELM, dealing with forward selection and backward elimination of hidden neurons. In forward selection, hidden nodes are selected in groups and this selection process terminates automatically when the predicted error reaches its minimum value. The selection of nodes is computed recursively. Dash, Dash, and Bisoi(2014) have proposed a Self-adaptive Differential Harmony Search based on Optimized Extreme Learning Machine (SADHS-OELM) for predicting the closing price of stock indices. Zeng, Zhang, Liu, and Alsaadi (2017) presented a hybrid model SDPSO-ELM for the short-term load forecasting of the power system. In order to make ELM to train the data in a dynamic way, a fast incremental ELM called bidirectional ELM was proposed by Yang, Wang, and Yuan (2012) to prune or replace hidden neurons and thus reduce the complexity of the network. The weights and biases between input and hidden neurons need to be optimized to get better accuracy within less computation time.