Forecasting cross-population innovation diffusion: A Bayesian approach

We introduce a cross-population, adaptive diffusion model that can be used to forecast the diffusion of an innovation at early stages of the diffusion curve. In this model, diffusion patterns across the populations depend on each other. We extend the model presented by Putsis, Balasubramanian, Kaplan and Sen (1997) [Putsis, W.P., Balasubramanian, S., Kaplan, E.H., Sen, S.K., 1997. Mixing behavior in cross-country diffusion. Marketing Science, 16 (4), 354–369.] by introducing time-varying parameters. Furthermore, we apply the matching procedure as proposed by Dekimpe, Parker and Sarvary (1998) [Dekimpe, M.G., Parker, Ph.M., Sarvary, M., 1998. Staged estimation of international diffusion models: An application to global cellular telephone adoption. Technological Forecasting and Social Change, 57 (1–2), 105–132.]. We adaptively estimate the model parameters using an extension of the augmented Kalman Filter with Continuous States and Discrete observations, developed by Xie, Song, Sirbu and Wang (1997) [Xie, J., Song, M., Sirbu, M., Wang, Q., 1997. Kalman filter estimation of new product diffusion models. Journal of Marketing Research, 34 (3), 378–393.]. We apply the method to the diffusion of both Internet access at home and mobile telephony among households in 15 countries of the European Union. The results show that forecasts obtained from our model outperform those from independent diffusion models for each country separately, as well as forecasts from the mixing-behavior model by Putsis et al. (1997).