Sales forecasting using longitudinal data models

This paper shows how to forecast using a class of linear mixed longitudinal, or panel, data models. Forecasts are derived as special cases of best linear unbiased predictors, also known as BLUPs, and hence are optimal predictors of future realizations of the response. We show that the BLUP forecast arises from three components: (1) a predictor based on the conditional mean of the response, (2) a component due to time-varying coefficients, and (3) a serial correlation correction term. The forecasting techniques are applicable in a wide variety of settings. This article discusses forecasting in the context of marketing and sales. In particular, we consider a data set of the Wisconsin State Lottery, in which 40 weeks of sales are available for each of 50 postal codes. Using sales data as well as economic and demographic characteristics of each postal code, we forecast sales for each postal code.