Statistical inference using stochastic switching models for the discrimination of unobserved non-price promotion

It is known that an execution of price and/or a non-price promotion has a strong influence on the sales of a brand sold in a supermarket. Usually, we can easily obtain information on a price promotion from a POS data. On the other hand, unless investigator collects information on an execution of non-price promotion in every retail store, we can not obtain such information. In this paper, we consider a problem to identify whether or not non-price promotion is conducted. We treat a non-price promotion execution/non-execution as a state variable. An unknown stationary probability matrix is assumed to describe the probability of a transition between states. Each state is characterized by a different stationary time series model with unknown parameters. An objective of the analysis is to identify the model and to assign a probability model for each state at each time instant. Finally, we give a high precision estimator of a past non-price promotion based on the proposal model.