An Auto-Regressive eXogenous input (ARX) model has been widely used in engineering fields to model dynamic response of a system to exogenous factors. A difficulty in this modeling is the determination of an appropriate model complexity, i.e., orders, for given data. In this paper, we develop a new and practical approach to determine the appropriate orders. Moreover, we apply the developed technique to a real marketing data, and analyze dynamic response character of sales amount to advertisement and sales promotion. In marketing study, static response of sales to some exogenous factors such as advertisement and sales promotion have been analyzed. However, if we can model dynamic response of sales to exogenous factors, more precise strategies of the sales to reduce the risk of the item stock management and increase the associated profit can be designed.