GJR-GARCH (Asymmetric GARCH)
Also known as: asymmetric GARCH, leverage GARCH, TGARCH, GJR-GARCH — Asimetrik GARCH (Glosten-Jagannathan-Runkle)
GJR-GARCH is a variant of the GARCH conditional-volatility model that captures the asymmetric effect of negative shocks on volatility using an indicator variable. It was introduced by Glosten, Jagannathan and Runkle (1993), with a closely related threshold formulation by Zakoian (1994).
Key highlights
- Captures the leverage effect — negative shocks raising volatility more than positive ones — through a simple, interpretable indicator term.
- Uses a linear formulation that is often easier to estimate and interpret than the log-variance EGARCH alternative.
- Nests the symmetric GARCH model as the special case γ = 0, so the asymmetry can be tested directly.
Intuition
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How it works
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When to use it
Use GJR-GARCH for financial return series that show volatility clustering and you expect negative shocks to drive volatility more than positive ones. It assumes an ARCH effect has already been detected in the residuals, that you are working with a financial-style return series, and that volatility clustering is present. A reasonably long series is needed — at least about 100 observations — and the leverage asymmetry should be a feature you actually want to model rather than impose.
Strengths & limitations
- Captures the leverage effect — negative shocks raising volatility more than positive ones — through a simple, interpretable indicator term.
- Uses a linear formulation that is often easier to estimate and interpret than the log-variance EGARCH alternative.
- Nests the symmetric GARCH model as the special case γ = 0, so the asymmetry can be tested directly.
- Requires a financial-style return series with a confirmed ARCH effect and visible volatility clustering; it is not a general-purpose regression tool.
- Needs a reasonably long sample (about 100 observations or more) for stable maximum-likelihood estimates.
- Only models conditional variance — the mean equation and the choice of innovation distribution must be specified separately and can affect the fit.
Common pitfalls
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Applications
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Frequently asked
How is GJR-GARCH different from ordinary GARCH?
Ordinary GARCH treats positive and negative shocks symmetrically. GJR-GARCH adds an indicator term that only activates after a negative shock, so losses can raise predicted volatility more than equally sized gains. When the asymmetry parameter γ is zero, GJR-GARCH collapses back to standard GARCH.
How does it relate to EGARCH?
Both capture the leverage effect, but EGARCH models the logarithm of variance, while GJR-GARCH stays in the variance level and adds a linear indicator term. The GJR formulation is often easier to interpret, though EGARCH guarantees positive variance without parameter constraints.
Do I need to check anything before fitting it?
Yes. GJR-GARCH assumes an ARCH effect is present, so you should confirm volatility clustering in the residuals first. It also expects a financial-style return series and a reasonably long sample of at least about 100 observations.
What does the asymmetry parameter γ tell me?
A positive and significant γ means negative shocks add more to next-period volatility than positive shocks of the same magnitude — direct evidence of a leverage effect. If γ is not significantly different from zero, the symmetric GARCH model is adequate.
Sources
- 1.Glosten, L. R., Jagannathan, R. & Runkle, D. E. (1993). On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, 48(5), 1779-1801.
- 2.Zakoian, J. M. (1994). Threshold Heteroskedastic Models. Journal of Economic Dynamics and Control, 18(5), 931-955.
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ScholarGate. (2026, June 1). GJR-GARCH. ScholarGate. https://scholargate.app/econometrics/gjr-garch