Consumer market has several characteristics in common such as repeat-buying over the relevant time frame, a large number of customers, and a wealth of information detailing past customer purchases. Analyzing the characterizations of repeat-buying is necessary to understand and adapt to dynamics of customer behaviors for company to survive in a continuously changing environment. The aim of this paper is to develop a methodology to detect the existence of repeat-buying behavior and discover the potential period of the repeat-buying behavior. We propose a new mathematical model to capture the characteristics of repeat-buying behavior. The algorithms based on our previous works then proposed to provide a scheme to discover periodicity and trends of the purchase. Two fundamental repeat-buying types have been identified and analyzed. Any repeat-buying scenarios can be expressed as the combination of the two fundamental types. The proposed mathematical model coupled with our prior works on cyclic modeling form a systematic process to uncover the characteristics of repeat-buying phenomenon. The experiments against a domestic consumer goods company are provided. The experimental results show that the proposed model can predict likely periodic purchase more precisely than previous studies.