Limit theory of quadratic forms of long-memory linear processes with heavy-tailed GARCH innovations

JOURNAL OF MULTIVARIATE ANALYSIS

卷:120

Article

Chan, Ngai Hang¹  Zhang, Rong-Mao² 

[1] Chinese Univ Hong Kong, Hong Hom, Hong Kong, Peoples R China

[2] Zhejiang Univ, Dept Math, Hangzhou, Zhejiang, Peoples R China

关键词: GARCH;    Heavy-tailed;    Linear process;    Long-memory;    Quadratic forms;   

DOI  :  10.1016/j.jmva.2013.04.007

来源: Elsevier

【 摘 要 】

Let X-t = Sigma(infinity)(j=0) c(j)epsilon(t-j) be a moving average process with GARCH (1, 1) innovations {epsilon(t)}. In this paper, the asymptotic behavior of the quadratic form Q(n) = Sigma(n)(j=1) Sigma(n)(s=1) b(t - s)XtXs is derived when the innovation {8t} is a long-memory and heavy-tailed process with tail index alpha, where {b(i)} is a sequence of constants. In particular, it is shown that when 1 < alpha < 4 and under certain regularity conditions, the limit distribution of Q(n) converges to a stable random variable with index alpha/2. However, when alpha >= 4, Q(n) has an asymptotic normal distribution. These results not only shed light on the singular behavior of the quadratic forms when both long-memory and heavy-tailed properties are present, but also have applications in the inference for general linear processes driven by heavy-tailed GARCH innovations. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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