Evaluating the Forecasting Accuracy of Advanced Non-Linear Models in Predicting Stock Index Movements Using Volatility Index (VIX): An Empirical Study in the U.S. Market

Abstract

                 This study evaluates the forecasting accuracy of advanced non-linear models in predicting stock index movements using the Volatility Index (VIX), with a focus on the U.S. market. The VIX, a widely recognized measure of market volatility, is considered a leading indicator of future stock market movements. To assess the forecasting power of the VIX, we employ a range of predictive models, including Long Short-Term Memory (LSTM) networks, Markov Switching GARCH (MS-GARCH), and Random Forest (RF) algorithms. The LSTM model, known for its ability to capture complex temporal dependencies in time-series data, is trained on sequences of 10 historical time steps. The model demonstrates strong predictive performance, achieving an RMSE of approximately 0.0099, with a significant reduction in training loss, highlighting its effectiveness in volatile market conditions.

In contrast, the MS-GARCH model, renowned for its capability to model regime-switching behaviors in volatility, produces excellent fit metrics such as AIC and BIC, though it relies on assumptions about the market's latent volatility regimes. Meanwhile, the Random Forest model, valued for its interpretability and ease of implementation, struggles to capture the sequential and dynamic nature of financial data, resulting in a comparatively higher predictive error. The findings underscore the superior performance of deep learning models, particularly LSTM, in forecasting stock index movements, driven by their ability to model the intricate relationships between market volatility and returns. This research contributes to the literature on volatility forecasting and suggests avenues for enhancing market prediction techniques using advanced non-linear models.