Forecasting the Diffusion of Innovation: A Stochastic Bass Model with Log-Normal and Mean-Reverting Error Process

IEEE Transactions on Engineering Management, 58 (2), 228-249, 2011

Posted: 30 Oct 2012

See all articles by Juho Kanniainen

Juho Kanniainen

Tampere University

Saku Mäkinen

Tampere University of Technology - Department of Industrial Management

Robert Piche

affiliation not provided to SSRN

Alok Chakrabarti

Tampere University of Technology

Date Written: May 1, 2011

Abstract

Forecasting the diffusion of innovations plays a major role in managing technology development and in engineering management overall. In this paper, we extend the conventional Bass model stochastically by specifying the error process of sales as log-normal and mean-reverting. Our model satisfies the following reasonable properties, which are generally ignored in the existing literature: sales cannot be negative, the error process can have a memory, and sales fluctuate more when they are high and less when they are low. The conventional and widely used model that assumes normally distributed error term does not have these properties. We address how to forecast properly under the log-normal and mean-reverting error process, and show analytically and numerically that in our extended model sales forecasts can substantially alter conventional Bass forecasts. We also analyze the model empirically, showing that our extension can improve the accuracy of future sales forecasts.

Keywords: diffusion models, innovation forecasting, stochastic processes

Suggested Citation

Kanniainen, Juho and Mäkinen, Saku and Piche, Robert and Chakrabarti, Alok, Forecasting the Diffusion of Innovation: A Stochastic Bass Model with Log-Normal and Mean-Reverting Error Process (May 1, 2011). IEEE Transactions on Engineering Management, 58 (2), 228-249, 2011, Available at SSRN: https://ssrn.com/abstract=2168049

Juho Kanniainen (Contact Author)

Tampere University ( email )

P.O. 541, Korkeakoulunkatu 8 (Festia building)
Tampere, FI-33101
Finland

HOME PAGE: http://https://sites.google.com/site/juhokanniainen/

Saku Mäkinen

Tampere University of Technology - Department of Industrial Management ( email )

P.O. 541, Korkeakoulunkatu 8 (Festia building)
Tampere, FI-33101
Finland

Robert Piche

affiliation not provided to SSRN

Alok Chakrabarti

Tampere University of Technology ( email )

P.O. 541, Korkeakoulunkatu 8 (Festia building)
Tampere, FI-33101
Finland

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