Abstract

This study proposes a novel hybrid mathematical framework that integrates the Time-Varying Parameter Vector Autoregression (TVP-VAR) connectedness approach with Long Short-Term Memory (LSTM) deep learning networks to analyze, forecast, and manage volatility spillovers in green financial markets. The framework is motivated by the increasing complexity of risk transmission across sustainable assets, including green bonds, renewable energy stocks, carbon markets, and conventional energy assets. The proposed methodology follows a two-stage structure. First, the TVP-VAR model is employed to quantify dynamic connectedness and time-varying spillover effects across markets. Second, the extracted connectedness measures are used as inputs to an LSTM network to forecast future systemic risk dynamics and generate forward-looking variance–covariance matrices for portfolio optimization and hedging purposes. Using daily data from 2015 to 2025, the empirical results reveal that renewable energy stocks are the dominant transmitters of volatility within the system, exerting substantial spillover effects on green bonds and other sustainable assets. The forecasting evaluation demonstrates that the proposed hybrid TVP-VAR-LSTM framework significantly outperforms traditional econometric models (ARIMA and GARCH) as well as conventional machine-learning benchmarks (SVR, Random Forest, and XGBoost), reducing the Root Mean Squared Error (RMSE) by more than 46% in out-of-sample forecasting. Moreover, the enhanced forecasting accuracy translates into economically meaningful benefits, leading to substantial reductions in realized portfolio risk and improved hedging effectiveness. The findings further highlight the importance of carbon pricing mechanisms and standardized green bond certification in mitigating volatility transmission across sustainable financial markets. Overall, this study contributes to the literature on financial mathematics, systemic risk modeling, and machine learning in green finance by providing a unified framework for volatility spillover analysis, forecasting, and dynamic portfolio optimization.

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