GARCH(1,1) Explorer

GARCH(1,1) Parameters

σ_t² = ω + αε_t−1² + βσ_t−1²

Variance Equation

ω (constant) 0.02

α (shock impact / ARCH term) 0.08

β (persistence / GARCH term) 0.90

Persistence Summary

α + β

0.98

Unconditional σ²

1.00

Half-life of a variance shock

34 periods

Shock Experiment

Inject one large shock partway through the sample and watch the conditional variance spike and decay.

Shock size (in σ units) 3.0

Covariance-stationary: α + β < 1.

Simulated Returns (volatility clustering)

Conditional Standard Deviation σ_t (dashed line = unconditional σ)