Even in the information technology era,firms also face the problem of incomplete information.That is,firms have a complete internal database about when and what consumers purchase from their own firms,but they do not know much about external information such as when and what consumers choose from their competitors’ store.Previous papers infer consumer category-level purchase timing through consumer purchase information from one specific firm.However,they do not deal with consumer brand choice in the perspective of incomplete information.Therefore,this paper proposes a model that uses consumer purchase data from one firm to infer consumer purchase timing and brand choice from competitors.We use the difference between consumer category level interpurchase time and observed firm level interpurchase time to infer consumer interpurchase time from competitors.We use the interdependence between consecutive purchase occasions on brand choices to infer consumer brand choice from competitors.