A Hybrid ARIMA–EGARCH–Artificial Neural Network Model for Optimal Time Series Forecasting

Abstract

Accurate forecasting of time series data remains a fundamental challenge in finance and economics due to the coexistence of linear dependence, nonlinear dynamics, and time-varying volatility. Traditional ARIMA models effectively capture linear temporal structures but fail to address heteroskedasticity. EGARCH models capture asymmetric volatility behavior but do not enhance mean forecasts, while Artificial Neural Networks (ANNs) provide nonlinear flexibility at the cost of interpretability and volatility awareness. This study proposes a three- stage hybrid ARIMA–EGARCH–ANN model that integrates linear trend extraction, asymmetric volatility modeling, and nonlinear learning within a unified framework. Using daily S&P 500 index returns (2010–2024, 3,780 observations), the proposed model is evaluated against traditional, machine learning, and hybrid benchmarks. Empirical results show that the hybrid model achieves a MAPE of 3.82%, outperforming ARIMA by 27.4% and ANN by 18.6% in out-of-sample forecasting. Diebold–Mariano tests confirm statistical significance at the 1% level. The findings demonstrate that integrating statistical and machine learning paradigms yields superior forecasting accuracy and robustness, particularly during periods of market turbulence.