A Deep Spatio-Temporal Volatility Forecasting Framework Using ۳D-CNN–Transformer Fusion with Cross-Market Shock Propagation Analysis: Evidence from S&P ۵۰۰, FTSE ۱۰۰, and DAX

This paper introduces a deep spatio-temporal volatility forecasting framework that integrates ۳D-CNNs and Transformer architectures to capture multi-scale temporal patterns, nonlinear cross-market contagion, and latent shock-propagation dynamics. Using daily returns from the S&P ۵۰۰, FTSE ۱۰۰, and DAX, a high-dimensional volatility tensor is constructed from lagged returns, realized volatility, wavelet components, and cross-correlation maps. A ۳D-CNN extracts local temporal–spectral features, while a Transformer models long-range dependencies and asymmetric spillovers. Compared with MGARCH, long-memory, hybrid, and deep learning models, the proposed method achieves superior RMSE, QLIKE, and robustness, revealing strong US-to-Europe volatility spillovers and notable structural breaks.

کلیدواژه ها:

Volatility Forecasting ، Deep Learning ، Cross-Market Contagion ، ۳D Convolutional Neural Networks (۳D-CNN) ، Transformer Models