The Effect of Serial Correlation on Tests for Parameter Change at Unknown Time
| Autor: | S. M. Tang, I. B. MacNeill |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 1993 |
| Předmět: |
Statistics and Probability
62E20 residuals processes Stationary process Serial correlation Autocorrelation Regression analysis White noise cumulative sums change-point statistics Moment (mathematics) 62M15 Sample size determination 62J05 partial sums Statistics Linear regression spectral density 62M10 Statistics Probability and Uncertainty Random variable Mathematics 62G10 |
| Zdroj: | Ann. Statist. 21, no. 1 (1993), 552-575 |
| Popis: | 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 {2i- f(O)/fJr, f(A) dA), 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. 1. Introduction. Stochastic models for time sequenced data are generally characterized by several unknown parameters. These parameters may change over time, and if the changes, when they occur, do so unannounced and at unknown time points, then the associated inferential problem is referred to as the change-point problem. Various important application areas of statistics involve change detection in a central way; two of these areas are quality assurance and environmental monitoring. Most of the statistics commonly applied to the change-point problem involve cumulative sums or partial sums of regression residuals. The distribution theory for these statistics has been computed under the assumption that the error process for the regression model is white noise. In this paper we consider linear regression of a random variable against general nonstochastic functions of time, but with error variables that form a serially correlated time series. We then examine the large sample properties of the stochastic processes defined by the partial sums of the regression residuals. Large sample distribution theory for fixed sample size statistics used to detect changes in regression parameters is usually derived by computing the distributions of various functionals on |
| Databáze: | OpenAIRE |
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