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.
