Change point analysis of a Gaussian model

In this paper, the testing and estimation of a single change point in means and variances of a sequence of independent Gaussian normal random variables are studied. The Schwarz Information Criterion, SIC, is used to search for the change point. The unbiased version of the SIC for this change point problem is also derived for the finite sample case. Other properties of the SIC test statistic are given as well. Finally, two examples are given at the end of this paper to illustrate the method proposed, and changes are successfully detected.