Self-weighted least absolute deviation estimation for infinite variance autoregressive models

• 成果类型: Article
• 署名作者: Ling, SQ
• 署名单位: Hong Kong University of Science & Technology
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2005.00507.x
• 发表日期: 2005
• 页码: 381-393
• 关键词: parameter-estimation; limit theory; arma models; regression; quantiles; ARCH

摘要

How to undertake statistical inference for infinite variance autoregressive models has been a long-standing open problem. To solve this problem, we propose a self-weighted least absolute deviation estimator and show that this estimator is asymptotically normal if the density of errors and its derivative are uniformly bounded. Furthermore, a Wald test statistic is developed for the linear restriction on the parameters, and it is shown to have non-trivial local power. Simulation experiments are carried out to assess the performance of the theory and method in finite samples and a real data example is given. The results are entirely different from other published results and should provide new insights for future research on heavy-tailed time series.