Forecasting the realized volatility of stock price index: A hybrid model integrating CEEMDAN and LSTM

The realized volatility (RV) financial time series is non-linear, volatile, and noisy. It is not easy to accurately forecast RV with a single forecasting model. This paper adopts a hybrid model integrating Long Short-Term Memory (LSTM) and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to forecast the RV of CSI300, S&P500, and STOXX50 indices. After the empirical study, four loss functions MSE, MAE, HMSE, HMAE, and the model confidence set (MCS) test are taken as the evaluation criteria. This paper selected Back Propagation Neural Networks (BP), Elman Neural Networks (Elman), Support Vector Regression Machine (SVR), autoregression (AR), heterogeneous autoregressive (HAR), and their hybrid models with CEEMDAN as the comparison. The test results show that CEEMDAN-LSTM has the best performance in forecasting RV in emerging and developed markets. Besides, the performance of single models is inferior to their corresponding hybrid models with CEEMDAN. And the empirical results are robust with the “sliding window” approach.