Testing for changes in polynomial regression

TL;DR

This paper develops a statistical test for detecting structural breaks in polynomial regression models, providing an easy-to-apply method with reliable size and power properties even in small samples.

Contribution

It derives the asymptotic distribution of a maximum-type test statistic for structural change in polynomial regression, enhancing testing accuracy.

Findings

Test statistic has a known extreme value distribution.

The test performs well in small samples.

It effectively detects structural breaks.

Abstract

We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value distribution of a maximum-type test statistic which is asymptotically equivalent to the maximally selected likelihood ratio. The resulting test is easy to apply and has good size and power, even in small samples.