Stock index volatility forecasting based on novel CEEMDAN-LSTM-BN model

Long-short Term Memory (LSTM) is a state-of-art and widely used model to forecast financial time series. However, primitive LSTM networks do not perform well due to over-fitting problems of the deep learning model and non-linear and non-stationary characteristics of financial time series data. Thus, this paper proposed a novel hybrid network based on LSTM to solve the two problems. To avoid over-fitting, the modified LSTM-BN network consists of two LSTM layers, two Batch Normalization (BN) layers following each LSTM layer and a dropout layer. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is an outstanding data frequency decomposition technique which can decompose original time series into several intrinsic mode functions and a residue. The final prediction results are produced by rebuilding each predictive series after LSTM-BN processes each intrinsic mode function and residue. The advantages of the proposed networks are verified by comparing to primitive LSTM, other hybrid models and some famous machine learning models such as Support Vector Machine (SVM), Auto Regressive (AR) and Random Forest. Moreover, the robustness of the networks is assessed by numerical experiments on different stock indices datasets including “Standard's & Poor's 500 Index”, “Nikkei 255 Stock Index”, “Heng Seng Index” and “Deutscher Aktien Index”