###### Abstract
This approach balances forecasting accuracy and computational efficiency, making it well-suited for nonstationary and data-constrained financial time-series environments. Given the complex and nonlinear nature of financial time series--particularly volatility indices like the VX--traditional statistical models and even standard LSTM-based approaches often struggle to capture the full range of dynamic and multi-frequency patterns. To address these challenges, this study investigates a hybrid architecture that combines VMD, Cascaded LSTM layers, and a multi-head attention mechanism. Based on this motivation, this study is guided by the following research questions:  
* **RQ1:** Can the integration of VMD, Cascaded LSTM, and Attention mechanisms significantly enhance VIX forecasting accuracy compared to conventional deep learning models? * **RQ2:** Does the proposed hybrid model maintain robust predictive performance across different market regimes, such as periods of high versus low volatility? To empirically address these questions, we formulate the following hypotheses:
* **H1:** The VMD-Cascaded LSTM with Attention model yields statistically significantly lower forecasting errors (MSE and MAE) than standard LSTM-based benchmark models. * **H2:** The proposed model demonstrates stable performance across varying levels of market volatility. Our research findings significantly contribute to the existing literature. First, this study empirically evaluates the effectiveness of the VMD-Cascaded LSTM with the Attention model in predicting VIX volatility and demonstrates its potential to contribute significantly to volatility management and investment strategy formulation in financial markets. Second, the empirical results demonstrate that our model outperforms benchmark models, achieving substantial improvements in MSE, RMSE, and MAE, highlighting the effectiveness of integrating the Attention mechanism. Third, by leveraging the Attention mechanism within a sequential process, our model enhances its overall stability rather than merely listing machine learning methods, offering a more robust framework for volatility forecasting. These contributions provide valuable insights for volatility management and investment strategy formulation in financial markets. This study presents a VMD-Cascaded LSTM with the Attention model to improve market volatility forecasts, thereby enhancing risk management and investment strategies. Beyond finance, the architecture's adaptability extends to domains such as healthcare for early disease detection and climate science for flood risk forecasting. Moreover, in environments equipped with high-performance GPUs, the model can deliver even faster training and inference times. This enables investors and risk managers to reassess volatility forecasts for specific indices or financial instruments in near real time, supporting more agile and responsive decision-making. Such applicability underscores the model's potential integration into automated trading systems or real-time risk monitoring platforms. The remainder of this study is structured as follows. Section 2 provides a brief review of previous studies on financial forecasting using LSTM models and volatility prediction through machine learning techniques. Section 3 describes the dataset and outlines the proposed methodology. Section 4 presents the experimental results, highlighting the performance of the proposed model. Finally, Section 5 offers concluding remarks and discusses potential future research directions.