Learning about Stock Volatility: The Local Scale Model with Homoskedastic Innovations

The Local Scale Model of Shephard (1994) is a state-space model of volatility clustering similar in effect to IGARCH, but with an unobserved volatility that realistically evolves independently of the observed errors, instead of being mechanically determined by them. It has one fewer parameter to estimate than IGARCH, and a closed form likelihood, despite the unobservability of the volatility. Although the errors are assumed to be Gaussian conditional on the unobserved stochastic variance, they are Student t when conditioned on experience, with degrees of freedom that grow to a finite bound.