The development of a volatility model for an asset-return series consists of four steps:
- Build an ARMA time series model for the financial time series based on the serial dependence revealed by the ACF and PACF.
- Test the residuals of the model for ARCH/GARCH effects, again relying on the ACF and PACF for the series of the squared residual.
- Specify a volatility model if serial correlation effects are significant, and jointly estimate the mean and volatility equations.
- Check the fitted model carefully and refine it if necessary.
When applying volatility forecasting to return series, the serial dependence may be limited so that a constant mean may be used instead of an ARMA model.
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