Change-Point Monitoring in Linear Models

31 Pages Posted: 1 Nov 2006

See all articles by Alexander Aue

Alexander Aue

Clemson University

Lajos Horváth

University of Utah - Department of Mathematics

Marie Huaková

Charles University in Prague

Piotr Kokoszka

Utah State University - Department of Mathematics & Statistics

Abstract

We consider a linear regression model with errors modelled by martingale difference sequences, which include heteroskedastic augmented GARCH processes. We develop asymptotic theory for two monitoring schemes aimed at detecting a change in the regression parameters. The first method is based on the CUSUM of the residuals and was studied earlier in the context of independent identically distributed errors. The second method is new and is based on the squares of prediction errors. Both methods use a training sample of size m. We show that, as m →∞, both methods have correct asymptotic size and detect a change with probability approaching unity. The methods are illustrated and compared in a small simulation study.

Suggested Citation

Aue, Alexander and Horváth, Lajos and Huaková, Marie and Kokoszka, Piotr, Change-Point Monitoring in Linear Models. Econometrics Journal, Vol. 9, No. 3, pp. 373-403, November 2006. Available at SSRN: https://ssrn.com/abstract=941528 or http://dx.doi.org/10.1111/j.1368-423X.2006.00190.x

Alexander Aue (Contact Author)

Clemson University ( email )

101 Sikes Ave
Clemson, SC 29634
United States

Lajos Horváth

University of Utah - Department of Mathematics ( email )

1645 E. Campus Center
Salt Lake City, UT 84112
United States
801 581-8159 (Phone)

Marie Huaková

Charles University in Prague ( email )

Celetná 13
Praha 1, 116 36
Czech Republic

Piotr Kokoszka

Utah State University - Department of Mathematics & Statistics ( email )

3900 Old Main Hill
Logan, UT 84322-3530
United States
435-797-0746 (Phone)
435-797-1822 (Fax)

HOME PAGE: http://www.math.usu.edu/~piotr/

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