Financial Time Series Forecasting: A Hybrid Approach Combining AR-GARCH and Machine Learning Models

Accurately forecasting financial markets remains a central challenge in economics due to the volatile, nonlinear, and complex nature of asset price movements. Traditional statistical models like Autoregressive Generalized Autoregressive Conditional Heteroskedasticity (AR-GARCH) have been widely used for modeling volatility, but often fall short when addressing intricate market patterns. This study systematically compares the predictive capabilities of AR-GARCH, Long Short-Term Memory (LSTM) networks, Convolutional Neural Networks (CNN), Random Forest (RF), and a hybrid ensemble on weekly data from the S&P 500, FTSE 100, and Nikkei 225 indices spanning 2000 to 2024. Performance is evaluated using standard forecasting metrics: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The findings indicate that while each separate model has varying strengths depending on market conditions, the hybrid model consistently achieves superior accuracy by leveraging the diversity of all approaches. These results highlight the benefits of integrating classical econometric approaches with contemporary machine learning techniques to improve forecasting precision and strengthen the robustness of models in financial time series analysis.