Explanation
In GARCH models, the speed of mean reversion is determined by the persistence parameter, which is the sum of the ARCH (Ξ±) and GARCH (Ξ²) coefficients: Ξ± + Ξ².
- Model A: Ξ± = 0.03, Ξ² = 0.96 β Persistence = 0.03 + 0.96 = 0.99
- Model B: Ξ± = 0.02, Ξ² = 0.95 β Persistence = 0.02 + 0.95 = 0.97
- Model C: Ξ± = 0.01, Ξ² = 0.97 β Persistence = 0.01 + 0.97 = 0.98
- Model D: Ξ± = 0.01, Ξ² = 0.98 β Persistence = 0.01 + 0.98 = 0.99
Key Insight: The lower the persistence (Ξ± + Ξ²), the faster the model reverts to its long-run mean variance. The long-run mean variance is calculated as Ο / (1 - Ξ± - Ξ²), where Ο 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.