## The Annals of Statistics

### The Effect of Serial Correlation on Tests for Parameter Change at Unknown Time

#### Abstract

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.

#### Article information

Source
Ann. Statist. Volume 21, Number 1 (1993), 552-575.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176349042

Digital Object Identifier
doi:10.1214/aos/1176349042

Mathematical Reviews number (MathSciNet)
MR1212193

Zentralblatt MATH identifier
0771.62072

JSTOR
links.jstor.org

#### Citation

Tang, S. M.; MacNeill, I. B. The Effect of Serial Correlation on Tests for Parameter Change at Unknown Time. Ann. Statist. 21 (1993), no. 1, 552--575. doi:10.1214/aos/1176349042. http://projecteuclid.org/euclid.aos/1176349042.