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March, 1993 The Effect of Serial Correlation on Tests for Parameter Change at Unknown Time
S. M. Tang, I. B. MacNeill
Ann. Statist. 21(1): 552-575 (March, 1993). DOI: 10.1214/aos/1176349042


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 ${2\pi f(0)/\int^\pi_-\pi f(\lambda)d\lambda}$, where $f(\centerdot)$ is the spectral density of the noise process; in sample survey work this is know 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.


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S. M. Tang. I. B. MacNeill. "The Effect of Serial Correlation on Tests for Parameter Change at Unknown Time." Ann. Statist. 21 (1) 552 - 575, March, 1993.


Published: March, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0771.62072
MathSciNet: MR1212193
Digital Object Identifier: 10.1214/aos/1176349042

Primary: 62M10
Secondary: 62E20 , 62G10 , 62J05 , 62M15

Keywords: change-point statistics , cumulative sums , partial sums , residuals processes , serial correlation , Spectral density

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 1 • March, 1993
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