THE EFFECT OF SERIAL-CORRELATION ON TESTS FOR PARAMETER CHANGE AT UNKNOWN TIME

• 成果类型: Article
• 署名作者: TANG, SM; MACNEILL, IB
• 署名单位: Western University (University of Western Ontario)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349042
• 发表日期: 1993
• 页码: 552-575
• 关键词: likelihood ratio test; linear-regression; change-point; POLYNOMIAL REGRESSION; ASYMPTOTIC THEORY; cusum tests; models; performance; constancy; RESIDUALS

摘要

It is shown that serial correlation can produce striking effects in distributions of change-point statistics. Failure to account for these effects is shown to invalidate change-point tests, either through increases in the type 1 error rates if low frequency spectral mass predominates in the spectrum of the noise process, or through diminution of the power of the tests when high frequency mass predominates. These effects are characterized by the expression (2pif(0)/integral-pi/-pi f(lambda)dlambda}, where f(.) is the spectral density of the noise process; in sample survey work this is known as the design effect or ''deff.'' Simple precise adjustments to change-point test statistics which account for serial correlation are provided. The same adjustment applies to all commonly used regression models. Residual processes are derived for both stationary time series satisfying a moment condition and for general linear regression models with stationary error structure.