ARCH and GARCH Volatility Models

Article QuantStart

Summary

This article introduces conditional heteroskedasticity: periods of high return variance can cluster, even when a return series’ ordinary correlogram resembles white noise. ARCH models represent changing variance using past squared shocks, while GARCH models add lagged variance terms, giving a more persistent variance process. The discussion connects volatility forecasts to financial applications such as risk measurement, leverage decisions, and options valuation.

The proposed diagnostic is to first fit an appropriate model for the conditional mean, then examine the autocorrelation of its squared residuals. Serial dependence there suggests a volatility model may be useful. The article illustrates the workflow on FTSE 100 log returns: an ARIMA fit leaves apparent dependence in squared residuals, while a fitted GARCH model makes both ordinary and squared residual correlograms appear more like white noise. This is evidence of improved residual behavior, not proof of profitable forecasts. Model suitability depends on removing trends and mean dependence first, and the article leaves return forecasting and strategy construction for later work.

Key ideas

ARCH models make conditional variance depend on past squared shocks, while GARCH also uses past variance estimates.
Volatility clustering can be difficult to detect from the return series’ ordinary correlogram alone.
After modeling the conditional mean, autocorrelation in squared residuals can indicate remaining conditional variance structure.
The FTSE example reports that a GARCH fit reduces visible dependence in squared residuals.
A better residual fit does not by itself demonstrate forecast accuracy or trading profitability.

Using ARCH and GARCH to Model Volatility Clustering in Financial Returns

Summary

Key ideas

Tags