Modeling purchases as repeated events

We put forward a statistical model for interpurchase times that takes into account all the current and past information available for all purchases as time continues to run along the calendar timescale. It delivers forecasts for the number of purchases in the next period and for the timing of the first and consecutive purchases. Purchase occasions are modeled in terms of a counting process, which counts the recurrent purchases for each household as they evolve over time. We show that formulating the problem as a counting process has many advantages, both theoretically and empirically. We illustrate our model for yogurt purchases and we highlight its useful managerial implications.