Generalized Autoregressive Conditional Heteroskedasticity
Source: Bollerslev, T. (1986). Journal of Econometrics 31(3), 307–327.
TL;DR
Generalizes Engle's ARCH to GARCH by letting the conditional variance depend on its **own past
values as well as past squared shocks. The result is dramatically more parsimonious: GARCH(1,1)** —
just three parameters — captures the slowly decaying volatility persistence seen in nearly all financial
return series, and remains the default volatility model in practice.
What it documents (models)
ARCH needed many lags to fit persistent volatility; GARCH adds lagged conditional variances, giving an
ARMA-like structure for variance that fits long memory in volatility with few parameters.
The model
σ²_t = ω + α ε²_{t-1} + β σ²_{t-1} (GARCH(1,1)). The sum α + β measures volatility persistence
(close to 1 for most assets); ω/(1 − α − β) is the long-run variance the process mean-reverts toward.
Why it matters
benchmark every richer model must beat (Hansen-Lunde: for many series, nothing does).