Essentials of Time Series for Financial Applications

Figure 7.2 Observed and fitted log-squared S&P 500 returns.

Ruiz (1994) shows that the QML estimator applied to Eq. (7.25), when ${\upsilon }_t\mathrm{IID}{\chi }_1^2$ is replaced by ${\upsilon }_t\mathrm{IID}N(0,4.935)$, is consistent and asymptotically normal. However, the QML procedure is inefficient, as the method does not rely on the exact likelihood of $\ln R_t^2$. The approximation may occasionally ...