Censored Demand Estimation in Retail

Our goal is to estimate the true demand of a product at a given store location and time period in the retail environment based on a single noisy and potentially censored observation. We introduce a framework to make inference from multiple time series. Somewhat surprisingly, we establish that the algorithm introduced for the purpose of “matrix completion” can be used to solve the relevant inference problem. Specifically, using the Universal Singular Value thresholding (USVT) algorithm, we show that our estimator is consistent: the average mean squared error of the estimated average demand with respect to the true average demand goes to 0 as the number of store locations and time intervals become large. We establish other naturally appealing properties of the resulting estimator and using a real dataset in retail (Walmart), argue for the practical relevance of our approach. Various classical time series models can be considered special cases of the framework introduced. For this reason, we believe that this method may have broader implications beyond the current application.