Generalized Autoregressive Conditional Heteroskedasticity (GARCH)
Generalized Autoregressive Conditional Heteroskedasticity · Also known as: GARCH(1,1), generalized ARCH, conditional volatility model, GARCH Modeli
GARCH is an econometric model for the time-varying volatility of financial time series, introduced by Tim Bollerslev in 1986 as a generalisation of Engle's ARCH model. It treats the conditional variance as a function of past squared shocks and past variances, capturing the volatility clustering seen in returns.
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When to use it
Use GARCH for continuous financial time series that show volatility clustering, when forecasting or predicting conditional variance is the goal. It requires evidence of an ARCH effect (a significant ARCH-LM test) and a reasonably long series; the model needs at least about 100 observations, and reliable estimation of the persistence (α+β) typically needs several hundred. It is not appropriate when there is no ARCH effect, when the series is too short, or when shocks affect volatility asymmetrically.
Strengths & limitations
- Captures volatility clustering and time-varying conditional variance that constant-variance models miss.
- Parsimonious: the GARCH(1,1) form summarises rich volatility dynamics with very few parameters.
- Provides direct conditional-variance forecasts that are central to risk measures, option pricing, and value-at-risk.
- Symmetric GARCH treats positive and negative shocks identically, so it misses the leverage effect where bad news raises volatility more than good news.
- Needs a long series: with fewer than about 250 observations the parameters, especially the persistence α+β, are estimated unreliably and maximum likelihood may fail to converge.
- Is pointless when there is no ARCH effect — if volatility does not cluster, GARCH only adds needless complexity.
Frequently asked
What does the GARCH(1,1) notation mean?
The numbers are the lag orders: GARCH(1,1) uses one lagged squared shock (the ARCH term) and one lagged conditional variance (the GARCH term). It is the most common specification because it captures persistent volatility with just a handful of parameters.
How do I know whether I need GARCH at all?
Run an ARCH-LM test on the residuals. If it is significant there is volatility clustering and GARCH is justified; if it is not significant the variance is effectively constant and a simpler model such as ARIMA is more appropriate.
What is the leverage effect and can plain GARCH handle it?
The leverage effect is the tendency of negative shocks to raise future volatility more than positive shocks of the same size. Symmetric GARCH cannot capture this because it depends only on squared errors; asymmetric extensions like EGARCH or GJR-GARCH are used instead.
How much data does GARCH need?
The model needs at least about 100 observations to fit, but reliable estimates of the parameters — especially the persistence α+β — typically require several hundred. With fewer than around 250 observations the maximum-likelihood estimates can be unstable or fail to converge.
Sources
- 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 1). Generalized Autoregressive Conditional Heteroskedasticity. ScholarGate. https://scholargate.app/en/econometrics/garch
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- ARIMAEconometrics↔ compare
- DCC-GARCHFinance↔ compare
- EGARCHEconometrics↔ compare
- Exponential SmoothingEconometrics↔ compare
- GJR-GARCHEconometrics↔ compare