Abstract: In financial time series analysis,testing the ARCH effect and determining the appropriate order value is one of the important topics. In this paper,the Bayes factor is employed to test the ARCH effect and choose the appropriate order value for ARCH models under Bayesian framework. A procedure for computing Bayes factor based on path sampling is established for this purpose. In the end,a real example is illustrated to demonstrate our proposed method.

Key words: ARCH models, ARCH effect, Bayes factor, financial time series, path sampling, model comparison