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LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises
Zhu, Ke1; Ling, Shiqing2
2015-06-01
Source PublicationJOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN0162-1459
Volume110Issue:510Pages:784-794
AbstractThis 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.
KeywordARMA(p, q) models Asymptotic normality G/ARCH noises Heavy-tailed noises LADE Random weighting approach Self-weighted LADE Sign-based portmanteau test Strong consistency
DOI10.1080/01621459.2014.977386
Language英语
Funding ProjectHong 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 Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000357437300025
PublisherAMER STATISTICAL ASSOC
Citation statistics
Cited Times:12[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20278
Collection国家数学与交叉科学中心
Affiliation1.Chinese Acad Sci, Inst Appl Math, Beijing, Peoples R China
2.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China
Recommended Citation
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.
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