Answer: The GARCH (1, 1) model.

## Explanation ### Model Formulas: - **EWMA**: $\sigma_n^2 = \lambda \sigma_{n-1}^2 + (1-\lambda)r_{n-1}^2$ - **GARCH(1,1)**: $\sigma_n^2 = \omega + \alpha r_{n-1}^2 + \beta \sigma_{n-1}^2$ ### Given Conditions: - Both models have the same parameter on $\sigma_{n-1}^2$ (same $\beta$) - $\sigma_{n-1}^2 = r_{n-1}^2$ - Current variance is above long-run variance ### Analysis: In GARCH(1,1), the long-run variance is $\frac{\omega}{1-\alpha-\beta}$. When current variance is above long-run variance, the GARCH model will forecast a lower variance than EWMA because: 1. GARCH has a **mean-reversion** component ($\omega$) that pulls the forecast back toward the long-run average 2. EWMA has **no mean-reversion** - it's a weighted average that doesn't revert to any long-term level 3. With current variance above long-run level, GARCH's mean-reversion effect will reduce the forecast compared to EWMA Therefore, **GARCH(1,1) will forecast lower volatility** than EWMA under these conditions.

Author: LeetQuiz Editorial Team