Regular and promotional sales in new product life-cycle: A competitive approach

In this paper, we consider the application of the Lotka-Volterra model with churn effects, LVch, (Guidolin and Guseo, 2015) to the case of a confectionary product produced in Italy and recently commercialized in a European country. Weekly time series, referring separately to quantities of regular and promotional sales, are available. Their joint inspection highlighted the presence of compensatory dynamics suggesting the study with the LVch to estimate whether competition between regular and promotional sales exists and how it affects product life-cycle. The study of sales under promotion with respect to regular ones represents a new way of dealing with promotional activities effects, whereas the innovation diffusion literature on new product growth has typically considered the effect of pricing and advertising through the generalized Bass model (Bass et al., 1994). In that model, the total amount of sales, regular plus promotional sales, is analyzed with a univariate approach, while price and advertising expenditures are used as exogenous inputs, without a feedback control. Conversely, exploiting the availability of two distinct time series and studying their interaction, our results show that competition has a symmetric character. Regular sales may access the residual market of those under promotion indicating the beneficial effect of promotional efforts, but the reverse effect is also present. Short-term forecasts on the evolution of the two series are then built with a two stage procedure based on an iterated SARMAX. The predicted values are further validated with observed real data. A comparison with Euler standard predictions is also performed.