An Intelligent Secondary Decomposition Framework for Enhanced Realized Volatility Forecasting Using Signal Processing and Deep Learning

Abstract

Forecasting realised volatility is essential for financial risk management, portfolio optimisation, and derivative pricing. However, financial time series exhibit non-linearity, non-stationarity, and long memory, making accurate prediction challenging. This study proposes a novel hybrid decomposition-ensemble framework named CEEMDAN-SE-VMD-GRU-BPNN to improve realised volatility forecasting for the DAX and SSE indices. The framework begins with Complete Ensemble Empirical Mode Decomposition with Adaptive Noise to decompose the volatility series into intrinsic mode functions. Sample entropy then categorises these functions into low-frequency, medium-frequency, and high-frequency components based on their complexity. To enhance computational efficiency, k-means clustering reduces the number of components. Variational Mode Decomposition, optimised by the Grey Wolf Optimiser, further refines the high-frequency components. Low-frequency components representing long-term trends are forecast using a backpropagation neural network, while medium-frequency and high-frequency components capturing short-term fluctuations are modelled with gated recurrent units. The final volatility prediction is obtained by linearly aggregating all component forecasts. The model is evaluated over one-day, five-day, and twenty-one-day forecasting horizons using six metrics: root mean squared error, mean absolute error, mean absolute percentage error, symmetric mean absolute percentage error, root mean squared logarithmic error, and the coefficient of determination. Statistical validation is performed using the Modified Diebold-Mariano test and the Model Confidence Set procedure. Empirical results demonstrate that the proposed framework consistently outperforms 14 benchmark models across both indices and all horizons, effectively capturing market dynamics and addressing the complexities of realised volatility. The framework offers practical insights for investors and regulators, supporting improved risk management and financial stability.