【主讲】Chor-yiu (CY) SIN 副教授 (国立清华大学)
【主题】On functional limits of short- and long-memory linear processes with GARCH(1,1) noises
【时间】2013年11月13日 (周三) 15：30-17：00
【地点】上海财经大学经济学院楼710室
【语言】英文
【摘要】This paper considers the short- and long-memory linear processes with GARCH (1,1) noises. The functional limit distributions of the partial sum and the sample autocovariances are derived when the tail index is in (0;2), equal to 2, and in (2;1), respectively. The partial sum weakly converges to a functional of -stable process when <2 and converges to a functional of Brownian motion when 2. When the process is of short-memory and <4, the autocovariances converge to functionals of =2-stable processes; and if 4, they converge to functionals of Brownian motions. In contrast, when the process is of long-memory, depending on and (the parameter that characterizes the long-memory), the autocovariances converge to either (i) functionals of =2-stable processes; (ii) Rosenblatt processes (indexed by, 1=2< <3=4); or (iii) functionals of Brownian motions. The rates of convergence in these limits depend on both the tail index and whether or not the linear process is short- or long-memory. Our weak convergence is established on the space of c adl ag functions on [0;1] with either (i) theJ 1 or theM1 Topology (Skorokhod, 1956); or (ii) the weaker form Stopology (Jakubowski, 1997).
