Hideaki KIM †a) , Noriko TAKAYA †b) , Nonmembers, and Hiroshi SAWADA † †c) , Member SUMMARY Improvements in information technology have made it easier for industry to communicate with their customers, raising hopes for a scheme that can estimate when customers will want to make purchases. Although a number of models have been developed to estimate the timevarying purchase probability, they are based on very restrictive assumptions such as preceding purchase-event dependence and discrete-time

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... ect of covariates. Our preliminary analysis of real-world data finds that these assumptions are invalid: self-exciting behavior, as well as marketing stimulus and preceding purchase dependence, should be examined as possible factors influencing purchase probability. In this paper, by employing the novel idea of hierarchical time rescaling, we propose a tractable but highly flexible model that can meld various types of intrinsic history dependency and marketing stimuli in a continuous-time setting. By employing the proposed model, which incorporates the three factors, we analyze actual data, and show that our model has the ability to precisely track the temporal dynamics of purchase probability at the level of individuals. It enables us to take effective marketing actions such as advertising and recommendations on timely and individual bases, leading to the construction of a profitable relationship with each customer. key words: self-exciting process, time-rescaling theorem, e-commerce, purchase behavior * Earlier versions of this work were presented at the 23rd ACM International Conference on Information and Knowledge Management (CIKM '14) [13] as a conference paper.