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Stock index forecasting is an important tool for both the investors and the government organizations. However, due to the inherent large volatility, high noise, and nonlinearity of the stock index, stock index forecasting has been a challenging task for a long time. This paper aims to develop a novel hybrid stock index forecasting model named BSO-GNN based on the brain storm optimization (BSO) approach and the grey neural network (GNN) model by taking full advantage of the grey model in dealing with data with small samples and the neural network in handling nonlinear fitting problems. Moreover, the new developed BSOGNN, which initializes the parameters in grey neural network with the BSO algorithm, has great capability in overcoming the deficiencies of the traditional GNN model with randomly initialized parameters through solving the local optimum and low forecasting accuracy problems. The performance of the proposed BSO-GNN model is evaluated under the normalization and nonnormalization preprocessing situations. Experimental results from the Shanghai Stock Exchange (SSE) Composite Index, the Shenzhen Composite Index, and the HuShen 300 Index opening price forecasting show that the proposed BSO-GNN model is effective and robust in the stock index forecasting and superior to the individual GNN model. [ABSTRACT FROM AUTHOR]