Abstract: In capitial asset pricing theory,it is a fundamental assumption that the extra returns of securities have constant variance. However,this assumption is not always realistic,thus it is necessary to check of this assumption. Under the Bayesian framework,the paper is devoted to constructing Bayesian test for the autoregression conditional heteroscadasicity (ARCH) of the CAPM with structural change. In the end,the effectiveness of the developed approach is illustrated with a real example.

Key words: ARCH, Bayes factor, CAPM, path sampling, structural change