“…A prominent feature of volatility is the presence of long memory, which led, within the GARCH framework, to the development of the integrated GARCH (Engle and Bollerslev (1986)), the fractionally integrated GARCH (Baillie, Bollerslev, and Mikkelsen (1996)) and the linear ARCH (Robinson (1991), Giraitis, Robinson, and Surgailis (2000)) models. With high frequency data, the long persistence in a series of realized volatilities is portrayed by a slow decay in the autocorrelation function (see e.g., Andersen and Bollerslev (1997), Andersen, Bollerslev, Diebold, and Ebens (2001)), and is modeled by means of fractionally integrated ARMA (ARFIMA) processes by Andersen, Bollerslev, Diebold, and Labys (2003), Oomen (2001) and Koopman, Jungbacker, and Hol (2005), among others.…”