Summary: A change-point problem in finite sequences is considered along with, so-called, \(k\)-linear-\(r\)-ahead recursive residuals and a test procedure proposed by J. A. Żołądź, Z. Szkutnik, J. Majerczak and K. Duda [Detection of change points in oxygen uptake during an incremental exercise test using recursive residuals: relationship to the plasma lactate accumulation and blood acid base balance. Europ. J. Appl. Physiol. 78, 369–377 (1998)]. Theoretical significance levels of that (conservative) test are compared with its simulated sizes. Numerical approximations to the powers against various alternatives are given. Properties of the \(k\)-linear-\(r\)-ahead recursive residuals are described and the consistency of the test is proved, when the noise level goes to zero.