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

• 成果类型: Article
• 署名作者: Zhu, Ke; Ling, Shiqing
• 署名单位: Chinese Academy of Sciences; Hong Kong University of Science & Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.977386
• 发表日期: 2015
• 页码: 784-794
• 关键词: least absolute deviation; time-series models; exponential likelihood estimators; infinite variance; garch processes; CONDITIONAL HETEROSCEDASTICITY; limiting distributions; regression-estimators; garch/igarch models; ASYMPTOTIC THEORY

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.