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Contaminated Renewal Processes and the Serial Correlogram

We derive the mean and variance of the sample serial correlation coefficients of a finite portion of a renewal process, the realization of which is contaminated by the addition or deletion of one point. This enables us to determine the asymptotic power of a test that the contaminated process is significantly different from a renewal process. In contrast to the signficant changes in serial correlation coefficient observed in simulations by Shiavi and Negin [1], our analysis shows that the expected differences are rather small. We discuss the work of ten Hoopen [2] which has a similar motivation.