Combining ANFIS and GARCH Models for Predicting Stock Index Returns

In the ever-evolving landscape of quantitative finance, predicting stock index returns remains a formidable challenge due to the intricate dynamics of financial markets. This chapter introduces a novel approach that combines the Adaptive Neuro-Fuzzy Inference System (ANFIS) with the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to capture the complex relationships and asymmetries in financial data. By replacing traditional square return measures with realized variance and kernel variance, derived from high-frequency data, the proposed model aims to enhance the accuracy of financial return forecasts. The empirical study, conducted using S&P 500 index data, demonstrates the superior performance of the hybrid model, particularly when employing the realized kernel estimator. The integration of genetic algorithms for parameter optimization further refines the model's predictive capabilities, making it a robust tool for navigating the volatile stock market. The chapter also explores the impact of different volatility estimators and the importance of asymmetry in financial modeling, providing valuable insights for improving forecasting techniques in quantitative finance.