Bootstrapping unit root tests for autoregressive time series

• 成果类型: Article
• 署名作者: Paparoditis, E; Politis, DN
• 署名单位: University of Cyprus; University of California System; University of California San Diego
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000001998
• 发表日期: 2005
• 页码: 545-553
• 关键词: SIEVE BOOTSTRAP; models; ORDER; POWER

摘要

The theory developed for bootstrapping unit root tests in an autoregressive (AR) context has been concerned mainly with the large-sample behavior of the methods proposed under the assumption that the null hypothesis is true. No results exist for the relative performance and the power behavior of the bootstrap methods under the alternative. This article studies the properties of different AR bootstrap schemes of the unit root hypothesis, including a new proposal based on unrestricted residuals. It shows that bootstrap procedures based on differencing the observed series suffer from power problems as compared with bootstrap procedures based on unrestricted residuals. Whereas for finite-order AR processes differencing leads to just a loss of power, for infinite-order autoregressions such a differencing makes the application of sieve AR bootstrap schemes inappropriate if the alternative is true. The superiority of the new bootstrap proposal is shown, and some numerical examples illustrate our theoretical findings.