LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises

doi:10.1080/01621459.2014.977386

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	LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises
	Zhu, Ke1 ; Ling, Shiqing 2
	2015-06-01
发表期刊	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN	0162-1459
卷号	110 期号:510 页码:784-794
摘要	This article develops a systematic procedure of statistical inference for the auto-regressive moving average (ARMA) model with unspecified and heavy-tailed heteroscedastic noises. We first investigate the least absolute deviation estimator (LADE) and the self-weighted LADE for the model. Both estimators are shown to be strongly consistent and asymptotically normal when the noise has a finite variance and infinite variance, respectively. The rates of convergence of the LADE and the self-weighted LADE are n(-1/2), which is faster than those of least-square estimator (LSE) for the ARMA model when the tail index of generalized auto-regressive conditional heteroskedasticity (GARCH) noises is in (0, 4], and thus they are more efficient in this case. Since their asymptotic covariance matrices cannot be estimated directly from the sample, we develop, the random weighting approach for statistical inference under this nonstandard case. We further propose a novel sign-based portmanteau test for model adequacy. Simulation study is carried out to assess the performance of our procedure and one real illustrating example is given. Supplementary materials for this article are available online.
关键词	ARMA(p, q) models Asymptotic normality G/ARCH noises Heavy-tailed noises LADE Random weighting approach Self-weighted LADE Sign-based portmanteau test Strong consistency
DOI	10.1080/01621459.2014.977386
语种	英语
资助项目	Hong Kong Research Grants Commission[HKUST641912] ; Hong Kong Research Grants Commission[HKUST603413] ; National Natural Science Foundation of China[11201459] ; National Natural Science Foundation of China[11371354] ; Academy of Mathematics and System Science, Chinese Academy of Sciences[2014-cjrwlzx-zk] ; Key Laboratory of RCSDS, Chinese Academy of Sciences
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000357437300025
出版者	AMER STATISTICAL ASSOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20278
专题	国家数学与交叉科学中心
通讯作者	Zhu, Ke
作者单位	1.Chinese Acad Sci, Inst Appl Math, Beijing, Peoples R China 2.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Zhu, Ke,Ling, Shiqing. LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2015,110(510):784-794.
APA	Zhu, Ke,&Ling, Shiqing.(2015).LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,110(510),784-794.
MLA	Zhu, Ke,et al."LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 110.510(2015):784-794.