EGARCH Model (Exponential GARCH)
Exponential Generalized Autoregressive Conditional Heteroscedasticity Model · Also known as: Exponential GARCH, EGARCH, Nelson EGARCH, log-GARCH
The Exponential GARCH (EGARCH) model, introduced by Nelson (1991), extends the standard GARCH framework by modelling the logarithm of conditional variance. This ensures variance is always positive without parameter constraints and, crucially, allows negative and positive shocks to have asymmetric effects on volatility — capturing the well-known leverage effect in financial markets.
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When to use it
Use EGARCH when modelling financial return series — equities, exchange rates, commodities, or cryptocurrencies — where volatility clustering is expected and asymmetric responses to positive versus negative shocks are likely. It is particularly valuable when testing for leverage effects or when GARCH fails because non-negativity constraints on parameters are binding. Avoid EGARCH for non-financial or low-frequency data where volatility clustering is absent, for very short series (fewer than 200–300 observations), or when a simpler ARCH/GARCH already fits well and the asymmetry parameter is insignificant.
Strengths & limitations
- Naturally ensures positive conditional variance without imposing parameter sign constraints, because it models log(sigma_t^2).
- Explicitly captures the leverage effect through the asymmetry (gamma) parameter, which is absent in standard GARCH.
- More flexible than symmetric GARCH and often provides a better fit to financial return data.
- The log specification makes the model robust to outliers and large shocks relative to standard GARCH.
- Numerical optimisation of the log-likelihood is more complex and sensitive to starting values than standard GARCH.
- The asymmetric log-variance equation is harder to interpret directly than the variance-level equation of standard GARCH.
- Requires reasonably long time series (at least 200–300 observations) for stable parameter estimates.
- Forecasting multi-step-ahead volatility is less straightforward on the log scale than in the variance-level GARCH.
- Model selection among GARCH family variants (EGARCH, TGARCH, GJR-GARCH) requires careful information-criterion comparison.
Frequently asked
What is the leverage effect and how does EGARCH model it?
The leverage effect is the empirical regularity that negative asset-return shocks raise subsequent volatility more than positive shocks of equal magnitude. In the EGARCH log-variance equation the gamma coefficient multiplies the signed standardised shock. A negative and significant gamma means bad news raises log-variance more than good news, directly quantifying the asymmetric response.
Why model log(sigma^2) instead of sigma^2 directly?
Working on the log scale guarantees that the conditional variance exp(ln(sigma_t^2)) is always positive, regardless of the sign of the estimated parameters. Standard GARCH must impose alpha, beta >= 0 to prevent negative variance; EGARCH imposes no such constraint, giving the optimizer more freedom.
How do I choose the order (p, q) for EGARCH?
Compare candidate EGARCH(p, q) specifications using AIC or BIC. In practice, EGARCH(1,1) fits most daily financial return series adequately. Inspect residual autocorrelation (Ljung-Box on squared standardised residuals) to confirm no remaining ARCH effects.
When should I prefer TGARCH (GJR-GARCH) over EGARCH?
Both model asymmetric volatility. TGARCH (Glosten-Jagannathan-Runkle) operates on the variance level and is simpler to interpret and forecast. EGARCH is preferred when non-negativity constraints are binding in the TGARCH estimation or when a log-scale model is theoretically motivated. Compare both with information criteria on your specific dataset.
What distribution should I assume for the innovation z_t?
A standard normal assumption is the starting point, but financial returns typically have heavier tails. Student-t or the Generalised Error Distribution (GED) often improve fit and produce more reliable VaR estimates. Test the chosen distribution with QQ-plots and formal goodness-of-fit statistics on the standardised residuals.
Sources
- Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370. DOI: 10.2307/2938260 ↗
- Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327. DOI: 10.1016/0304-4076(86)90063-1 ↗
How to cite this page
ScholarGate. (2026, June 3). Exponential Generalized Autoregressive Conditional Heteroscedasticity Model. ScholarGate. https://scholargate.app/en/econometrics/egarch-model
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