Vine copula-based optimal multivariate deep learning model with genetic algorithm optimization for time series forecasting

This study introduces a novel forecasting framework, a Vine Copula (VC)-based Multivariate Deep Learning (MDL) model optimized using a Genetic Algorithm (GA), referred to as the Optimal GA-MDL-VC model. The model leverages GA to fine-tune the hyperparameters of various MDL architectures, including Multivariate Long Short-Term Memory (MLSTM), Multivariate Gated Recurrent Unit (MGRU), and Multivariate Recurrent Neural Network (MRNN). The integration of Vine Copulas with these GA-MDL variants enables the model to effectively capture complex interdependencies among multiple time series, thereby enhancing forecasting accuracy. An empirical study using daily modal price data of soybean – a globally significant agricultural commodity – across 15 major Indian markets demonstrates the superior forecasting accuracy of the proposed Optimal GA-MDL-VC model. Performance was evaluated against GA-MDL and traditional Multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH) models using two data splits: 80:10:10 and 70:15:15 for training, validation, and testing. The Optimal GA-MDL-VC model consistently outperformed the other models.