Abstract
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 Żoła¸dź et al. [Żoła¸dź, J.A., Szkutnik, Z., Majerczak, J. and Duda, K. 1998, Detection of change point in oxygen uptake during an incremental exercise test using recursive residuals: relationship to the plasma lactate accumulation and blood acid base balance. European Journal of Applied Physiology, 78, 369–377.]. 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.
Acknowledgements
This research was partly supported by AGH local grant 10.420.03. The authors thank J.A. Żoła¸dź for the permission to use some real data from his physiological experiments for illustrative purposes. Suggestions of the reviewers of an early version of the manuscript are kindly acknowledged.