Answer: $ h_t = 0.03 + 0.02r_{t-1}^2 + 0.95h_{t-1} $

## Explanation In GARCH models, the speed of mean reversion is determined by the persistence parameter, which is the sum of the ARCH (α) and GARCH (β) coefficients: **α + β**. - **Model A**: α = 0.03, β = 0.96 → Persistence = 0.03 + 0.96 = 0.99 - **Model B**: α = 0.02, β = 0.95 → Persistence = 0.02 + 0.95 = 0.97 - **Model C**: α = 0.01, β = 0.97 → Persistence = 0.01 + 0.97 = 0.98 - **Model D**: α = 0.01, β = 0.98 → Persistence = 0.01 + 0.98 = 0.99 **Key Insight**: The **lower** the persistence (α + β), the **faster** the model reverts to its long-run mean variance. The long-run mean variance is calculated as ω / (1 - α - β), where ω is the constant term. - **Model B has the lowest persistence (0.97)**, meaning it will revert to its mean the fastest. - Models A and D have the highest persistence (0.99), meaning they take the longest to revert. - Model C has persistence of 0.98, which is higher than Model B. Therefore, **Model B** will take the shortest time to revert to its mean.

Author: LeetQuiz .