Quantile inference for near-integrated autoregressive time series under infinite variance and strong dependence

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Chan, Ngai Hang²  Zhang, Rong-Mao¹ 

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Chinese Univ Hong Kong, Dept Stat, Shatin, Hong Kong, Peoples R China

关键词: Heavy-tailed;    Long-range dependent;    Near-integrated time series and quantile regression;   

DOI  :  10.1016/j.spa.2009.09.010

来源: Elsevier

【 摘 要 】

Consider a near-integrated time series driven by a heavy-tailed and long-memory noise epsilon(t) = Sigma(infinity)(j=0)c(j)n(t-j), where {n(j)} is a sequence of i.i.d random variables belonging to the domain of attraction of a stable law with index a. The limit distribution of the quantile estimate and the semi-parametric estimate of the autoregressive parameters with long- and short-range dependent innovations are established in this paper. Under certain regularity conditions, it is shown that when the noise is short-memory, the quantile estimate converges weakly to a mixture of a Gaussian process and a stable Ornstein-Uhlenbeck (O-U) process while the semi-parametric estimate converges weakly to a normal distribution. But when the noise is long-memory, the limit distribution of the quantile estimate becomes substantially different. Depending on the range of the stable index alpha, the limit distribution is shown to be either a functional of a fractional stable O-U process or a mixture of a stable process and a stable O-U process. These results indicate that although the quantile estimate tends to be more efficient for infinite variance time series, extreme caution should be exercised in the long-memory situation. (C) 2009 Elsevier B.V. All rights reserved.

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