Likelihood ratio and cumulative sum tests for a change-point in linear regression

Our concern in this paper is a detection of a change in regression coefficients of a linear model. First, we examine the null and alternative distributions of the likelihood ratio statistic and study its asymptotic behavior. We then propose analytic approximations for the p-value and power of the test and perform simulations to assess the accuracy of the analytic approximations. Also, the test based on the cusum of the recursive residuals is discussed and its power is compared with that of the likelihood ratio test. We conclude that the likelihood ratio yest is much more powerful than the cusum test of Brown et al. (1975, J. Roy. Statist. Soc. Ser. B37, 149-192) and propose a test based on the backward cusum to improve the power of the cusum test.