Regular and promotional sales in new product life-cycles: Competition and forecasting

In this paper, we perform a joint analysis of regular (full price) and promotional (discounted price) sales of a product, on the hypothesis that the two sale processes can influence each other, whereas literature on new product growth has typically considered pricing and advertising expenditures as exogenously affecting total sales, with no distinction between regular and promotional. We suggest an approach based on a modified Lotka–Volterra model, which captures competition effects. We apply our method to real data of a confectionary product recently commercialized in a European country. Weekly time series, referring separately to regular and promotional sales, are available. Results show that competition actually exists and has a symmetric character: regular sales may access the residual market of those under promotion, indicating the beneficial effect of promotional efforts; however, the opposite effect is also significant. A new methodology based on a SARMA approximation of fitted nonlinear mean trajectories and further validated with observed real data allows out-of-sample forecasting and provides an indication of the timing of future promotional activities.