Threshold GARCH
Make the sign and power of volatility shocks explicit
Threshold volatility models let positive and negative innovations have different effects. The GJR specification commonly places an indicator on lagged squared innovations in the conditional variance equation. Zakoian’s TARCH models conditional standard deviation with sign-specific terms. Software sometimes calls either TGARCH, so the equation and power must be reported to make estimates and constraints interpretable.
Choose this when an asymmetric response can be represented by a sign threshold and the available history supports its estimation. Decide explicitly whether variance or standard deviation is being modelled.
Strengths
- Directly represents different responses by shock sign
- Provides a clear comparison with symmetric GARCH
Limitations
- TGARCH labels conceal materially different parameterisations
- Estimated asymmetry can be sensitive to outliers and distribution choice
Know the boundary
GJR-GARCH and Zakoian TARCH are related but not identical, even when software labels both TGARCH.