Testing for a linear MA model against threshold MA models

• 成果类型: Article
• 署名作者: Ling, SQ; Tong, H
• 署名单位: Hong Kong University of Science & Technology; University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000598
• 发表日期: 2005
• 页码: 2529-2552
• 关键词: least-squares estimator; likelihood ratio tests; ergodicity; autoregression; parameter; checks

摘要

This paper investigates the (conditional) quasi-likelihood ratio test for the threshold in MA models. Under the hypothesis of no threshold, it is shown that the test statistic converges weakly to a function of the centred Gaussian process. Under local alternatives, it is shown that this test has nontrivial asymptotic power. The results are based on a new weak convergence of a linear marked empirical process, which is independently of interest. This paper also gives an invertible expansion of the threshold MA models.