Analyzing Individual Purchasing Behavior Considering Interpurchase Time with Autocorrelation

In preceding research, an assumption about the independence of interpurchase time was made. Interpurchase time was assumed to be extracted independently from a particular distribution. However, autocorrelation is observed in interpurchase time and about 30% of the individuals' interpurchase time are well fitted using ARIMA model. Therefore, this study shows the effect of the dependence in interpurchase time, which affects the number of purchase in a certain unit time. First, we derive the distribution of the number of purchases in a certain unit time using some affordable assumption when interpurchase time follows particular ARIMA. Second, using simulation, we examine ARIMA model the number of purchase follows when the interpurchase time follows certain ARIMA model. Finally, we check the performance of analyzing ARIMA model of interpurchase time using the actual credit card usage data. Performance of using ARIMA of interpurchase time improves as the unit time and the number of purchase increases