Forecasting with limited data: Combining ARIMA and diffusion models

Forecasting diffusion of new technologies is usually performed by the means of aggregate diffusion models, which tend to monopolize this area of research and practice, making the alternative approaches, like the Box-Jenkins, less favourable choices due to their lack of providing accurate long-term predictions. This paper presents a new methodology focusing on the improvement of the short-term prediction that combines the advantages of both approaches and that can be applied in the early stages of a diffusion process. An application of the methodology is also illustrated, providing short-term forecasts for the world broadband and mobile telecommunications' penetration. The results reveal that the methodology is capable of producing improved one-year-ahead predictions, after a certain level of penetration, as compared to the results of both methods individually. This methodology can find applications to all cases of the high-technology market, where a diffusion model is usually used for obtaining future forecasts. The paper concludes with the limitations of the methodology, the discussion on the application's results and the proposals for further research.