TGARCH Model (Threshold GARCH)
Threshold Generalized Autoregressive Conditional Heteroscedasticity Model · Also known as: Threshold GARCH, TGARCH, GJR-GARCH, asymmetric GARCH
The Threshold GARCH (TGARCH) model extends the standard GARCH framework by allowing positive and negative return shocks to have asymmetric effects on conditional variance. Negative shocks — bad news — typically amplify volatility more than positive shocks of the same magnitude, a stylised fact known as the leverage effect. TGARCH captures this asymmetry through a threshold indicator that switches on when the previous period's shock was negative.
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When to use it
TGARCH is appropriate whenever you are modelling the conditional volatility of a financial or economic time series and suspect that negative shocks have a larger impact on volatility than positive shocks of the same size. It is well-suited to daily or weekly equity returns, exchange rates, commodity prices, and cryptocurrency returns where the leverage effect is common. Choose TGARCH over symmetric GARCH when a sign-bias test or ARCH-LM test residual analysis suggests asymmetry, or when economic theory predicts asymmetric risk responses. Avoid TGARCH when the series is stationary in variance and shows no evidence of ARCH effects; also avoid it for very short series (fewer than 250 observations), where the asymmetry parameter cannot be estimated reliably. If leverage effects appear in multiple assets simultaneously, DCC-GARCH or multivariate extensions may be more appropriate.
Strengths & limitations
- Directly captures the leverage effect through an interpretable threshold coefficient, revealing whether bad news amplifies volatility more than good news.
- Parsimonious extension of GARCH with only one additional parameter, keeping estimation tractable even in moderate samples.
- Produces superior out-of-sample volatility forecasts compared to symmetric GARCH when asymmetry is present.
- Straightforwardly nested within the GARCH family, allowing likelihood-ratio tests against symmetric GARCH as a special case (gamma = 0).
- Compatible with fat-tailed error distributions (Student-t, GED), improving fit to real financial return data.
- Requires at least 250 observations to estimate the asymmetry parameter with reasonable precision; shorter series yield unstable inference.
- Restricted to univariate volatility modelling; multivariate spillovers between assets require DCC-GARCH or related frameworks.
- Assumes a fixed parametric form for asymmetry; time-varying or nonlinear threshold effects may require regime-switching or Markov-switching GARCH extensions.
- Maximum likelihood estimation can converge to local optima; results should be checked with multiple starting values.
- Like all GARCH models, TGARCH does not directly explain the source of volatility clustering — it describes the pattern but not the underlying mechanism.
Frequently asked
What is the difference between TGARCH and EGARCH?
Both capture asymmetry in volatility responses, but EGARCH models the log of conditional variance, which automatically ensures non-negativity without parametric constraints. TGARCH models the variance level directly with a threshold indicator and requires constraints on the parameters. EGARCH can capture more flexible asymmetry shapes; TGARCH is easier to interpret and nest within the symmetric GARCH framework.
How do I test whether the asymmetry term is significant?
Examine the t-statistic (or z-statistic) on the estimated gamma coefficient in the variance equation. A significant positive gamma confirms the leverage effect. You can also conduct a likelihood-ratio test comparing the TGARCH model against a restricted symmetric GARCH model where gamma is constrained to zero.
What sample size is needed for reliable TGARCH estimation?
As a rule of thumb, at least 250 observations are needed to estimate the asymmetry parameter reliably. For daily financial data this corresponds to roughly one year of trading days. Shorter series risk unstable or poorly identified estimates of gamma.
Can TGARCH be extended to a multivariate setting?
The standard TGARCH is univariate. For multiple assets, DCC-GARCH or multivariate GARCH models with asymmetry components (such as the asymmetric DCC or the BEKK-GARCH) are the appropriate extensions, though they are considerably more complex to estimate.
Is GJR-GARCH the same as TGARCH?
They are very closely related. Both add a threshold term to the GARCH variance equation that activates on negative shocks, and they produce numerically identical conditional variances under equivalent parameterisations. The GJR-GARCH label comes from Glosten, Jagannathan, and Runkle (1993); the TGARCH label comes from Zakoian (1994). Some software distinguishes them by whether the threshold is applied to the shock level or its square.
Sources
- Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931-955. DOI: 10.1016/0165-1889(94)90039-6 ↗
- 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. Journal of Finance, 48(5), 1779-1801. DOI: 10.1111/j.1540-6261.1993.tb05128.x ↗
How to cite this page
ScholarGate. (2026, June 3). Threshold Generalized Autoregressive Conditional Heteroscedasticity Model. ScholarGate. https://scholargate.app/en/econometrics/tgarch-model
Which method?
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