典型文献
Nearly nonstationary processes under infinite variance GARCH noises
文献摘要：
Let Yt be an autoregressive process with order one,i.e.,Yt=μ+φnYt-1+εt,where{εt}is a heavy tailed general GARCH noise with tail index α.Let(φ)n be the least squares estimator(LSE)of φn.For μ=0 and α＜2,it is shown by Zhang and Ling(2015)that(φ)n is inconsistent when Yt is stationary(i.e.,φn ≡ φ＜1),however,Chan and Zhang(2010)showed that(φ)n is still consistent with convergence rate n when Yt is a unit-root process(i.e.,φn=1)and{εt}is a GARCH(1,1)noise.There is a gap between the stationary and nonstationary cases.In this paper,two important issues will be considered:(1)what about the nearly unit root case?(2)When can φ be estimated consistently by the LSE?We show that when φn=1-c/n,then(φ)n converges to a functional of stable process with convergence rate n.Further,we show that if limn→∞ kn(1-φn)=c for a positive constant c,then kn((φ)n-φ)converges to a functional of two stable variables with tail index α/2,which means that φn can be estimated consistently only when kn→∞.
文献关键词：
中图分类号：
作者姓名：
ZHANG Rong-mao;LIU Qi-meng;SHI Jian-hua
作者机构：
School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China;School of Mathematical Science,Zhejiang University,Hangzhou 310027,China
文献出处：
引用格式：
[1]ZHANG Rong-mao;LIU Qi-meng;SHI Jian-hua-.Nearly nonstationary processes under infinite variance GARCH noises)[J].高校应用数学学报B辑（英文版）,2022(02):246-257
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AB值：
0.495834
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