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. 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. The present paper improves on the Shephard model by assigning equal variance to the innovations to the volatility. The implied volatility gain at first declines sharply as in the classical Local Level Model, rather than being constant throughout as in traditional IGARCH (McCulloch 1985; Engle and Bollerslev 1986). The improved model is fit to monthly stock returns. The ML estimates imply 7.76 limiting degrees of freedom. A short-lived “Great Moderation†is evident during the mid-1990’s, but expires by 1998. Otherwise the period since 1970 was generally more volatile than the 1950s and 60s, though less so than the 1930s.