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- Publisher Website: 10.1080/01621459.2014.977386
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Article: LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises
Title | LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises |
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Authors | |
Keywords | Sign-based portmanteau test ARMA(p, q) models Asymptotic normality G/ARCH noises Heavy-tailed noises LADE Random weighting approach Self-weighted LADE Strong consistency |
Issue Date | 2015 |
Citation | Journal of the American Statistical Association, 2015, v. 110, n. 510, p. 784-794 How to Cite? |
Abstract | © 2015 American Statistical Association.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. |
Persistent Identifier | http://hdl.handle.net/10722/230993 |
ISSN | 2023 Impact Factor: 3.0 2023 SCImago Journal Rankings: 3.922 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Zhu, Ke | - |
dc.contributor.author | Ling, Shiqing | - |
dc.date.accessioned | 2016-09-01T06:07:20Z | - |
dc.date.available | 2016-09-01T06:07:20Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Journal of the American Statistical Association, 2015, v. 110, n. 510, p. 784-794 | - |
dc.identifier.issn | 0162-1459 | - |
dc.identifier.uri | http://hdl.handle.net/10722/230993 | - |
dc.description.abstract | © 2015 American Statistical Association.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 <sup>− 1/2</sup>, 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. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of the American Statistical Association | - |
dc.subject | Sign-based portmanteau test | - |
dc.subject | ARMA(p, q) models | - |
dc.subject | Asymptotic normality | - |
dc.subject | G/ARCH noises | - |
dc.subject | Heavy-tailed noises | - |
dc.subject | LADE | - |
dc.subject | Random weighting approach | - |
dc.subject | Self-weighted LADE | - |
dc.subject | Strong consistency | - |
dc.title | LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1080/01621459.2014.977386 | - |
dc.identifier.scopus | eid_2-s2.0-84936751255 | - |
dc.identifier.hkuros | 298378 | - |
dc.identifier.volume | 110 | - |
dc.identifier.issue | 510 | - |
dc.identifier.spage | 784 | - |
dc.identifier.epage | 794 | - |
dc.identifier.eissn | 1537-274X | - |
dc.identifier.isi | WOS:000357437300025 | - |
dc.identifier.issnl | 0162-1459 | - |