Testing for changes in polynomial regression
  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. 
Alexander Aue, Lajos Horv\'ath, Marie Hu\v{s}kov\'a, Piotr Kokoszka