ARCH and GARCH
Model clusters of high and low uncertainty
ARCH models conditional variance using past squared innovations. GARCH also includes lagged conditional variances, often representing persistence more parsimoniously. A separate mean equation remains necessary, and the innovation distribution controls tail behaviour. Standard symmetric specifications respond equally to positive and negative shocks of equal magnitude, unlike asymmetric variants such as EGARCH or threshold models.
Choose these for volatility clustering in returns or other time series when uncertainty changes over time. There must be sufficient temporal history to distinguish persistent variance dynamics from breaks and outliers.
Strengths
- Represents time-varying predictive uncertainty
- GARCH captures persistent volatility with relatively few parameters
Limitations
- Symmetric specifications miss sign-dependent responses
- Tail forecasts are sensitive to innovation distributions and breaks
Know the boundary
Volatility predictability is not return predictability. High persistence can reflect an unmodelled structural break.