4 - Scale

Summary

An established feature of asset returns is that they exhibit volatility clustering. Another stylized fact about returns is that their distributions typically have heavy tails. Although the Gaussian GARCH structure induces excess kurtosis in the returns, it is not usually enough to match the data. As a result, it is now customary to assume that returns have a conditional Student's t_v distribution. The GARCH-t model, which was originally proposed by Bollerslev (1987), is widely used in empirical work and as a benchmark for other models.

The t distribution in GARCH-t is employed in the predictive distribution of returns and used as the basis for maximum likelihood estimation of the parameters, but it is not acknowledged in the design of the equation for the conditional variance. The specification of the conditional variance as a linear combination of squared observations is taken for granted, but the consequences are that it responds too much to extreme observations, and the effect is slow to dissipate. These features of GARCH are well-known, and the consequences for testing and forecasting have been explored in a number of papers; see, for example, Franses, van Dijk and Lucas (2004). Other researchers, such as Sakata and White (1998) and Muler and Yohai (2008), have been prompted to develop procedures for robustification; see also Gregory and Reeves (2010).