the information set up till day t 1; gi;t is the short-term variance component; and mi;τ the longtermcomponent. Specially, the short-run variance component gi;t changes with the daily frequency t, and follows a GARCH(1,1) model,while the long-run variance component mi;τ is held fixed at the monthly frequency τ. The GARCH(1,1) model for short-run variance isspecified as follows: