Volatility forecasting for stock market index based on complex network and hybrid deep learning model

The existing literature on the volatility forecasting less considered the co‐movement among stock markets from the spatial dimension. This paper builds the hybrid convolutional neural networks (CNNs)–gated recurrent unit (GRU) model for volatility forecasting under high frequency financial data based on transaction information and the topological characteristics constructed through the complex network of multi‐market symbol patterns. The hybrid neural network CNN‐GRU combines the advantages of CNN automatically extracting features for the input indicators and GRU processing long and short‐term serially dependent features, which can better improve the forecasting accuracy. The empirical results show that with the integration of topological characteristics as the indicators based on complex network, the deep learning model has a significant improvement of one‐step and multi‐step volatility forecasting accuracy for the China's and the US stock markets. The research in this paper provides a complete index system from the spatial dimension and a more accurate and robust volatility forecasting method under the high‐frequency financial data.