Comparative Forecasting of Financial Time Series Using ARIMA, GARCH, Random Forest, and XGBoost Models

Accurate financial time series forecasting plays a crucial role in economics, investment decision-making, and risk management. This study conducts a comparative analysis of linear and nonlinear forecasting models applied to the S&P 500 daily closing prices. Specifically, the Autoregressive Integrated Moving Average (ARIMA), Generalized Autoregressive Conditional Heteroskedasticity (GARCH), Random Forest, and XGBoost models are evaluated using standard metrics including the Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE). Results indicate that while ARIMA performs effectively under linear dynamics, the GARCH model captures volatility clustering more accurately, and tree-based machine learning models such as Random Forest and XGBoost provide competitive predictive accuracy by learning nonlinear relationships. The study highlights the trade-offs between interpretability and predictive power, offering practical insights into the complementary use of statistical and machine learning methods for financial forecasting.