Abstract: This paper considers a likelihood ratio test for a change in mean when observations are not independent. First, the effect of correlation on the performance of the likelihood ratio test derived under the assumption of no correlation is examined. Then, the likelihood ratio statistic for testing for a change in mean is obtained under a general structure of nonzero correlation. For general correlation and some serial correlations such as AR (p), distributional properties of the test statistic are examined and methods to compute approximate p-values are discussed. Finally, the powe r of the likelihood ratio test is compared with that of the test proposed by Henderson (1986).
Key words and phrases: Approximate p-value, autoregressive process, boundary crossing probability, likelihood ratio test.