THE LIMIT DISTRIBUTION OF THE CUSUM OF SQUARES TEST UNDER GENERAL MIXING CONDITIONS

We consider the cumulative sum ~CUSUM! of squares test in a linear regression model with general mixing assumptions on the regressors and the errors+We derive its limit distribution and show how it depends on the nature of the error process+ We suggest a corrected version that has a limit distribution free of nuisance parameters+ We also discuss how it provides an improvement over the standard approach to testing for a change in the variance in a univariate times series+ Simulation evidence is presented to support this+