Forecasting product sales with a stochastic Bass model

With the Bass model and data of previous sales a point estimate of future sales can be made for the purpose of stock management. In order to obtain information about the accuracy of that estimate a confidence interval can be of use. In this study such an interval is constructed from a Bass model ext...

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Bibliographic Details
Published in:Journal of mathematics in industry 2019-02, Vol.9 (1), p.1-10, Article 2
Main Authors: Grasman, Johan, Kornelis, Marcel
Format: Article
Language:English
Subjects:
Applications of Mathematics
Bass model
Confidence domain
Confidence intervals
Math. Appl. in Environmental Science
Mathematical and Computational Biology
Mathematical and Computational Engineering
Mathematical Methods in Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Noise
Ornstein–Uhlenbeck process
Sales
Sensitivity of parameter to data
Time dependence
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Summary:With the Bass model and data of previous sales a point estimate of future sales can be made for the purpose of stock management. In order to obtain information about the accuracy of that estimate a confidence interval can be of use. In this study such an interval is constructed from a Bass model extended with a noise term. The size of the noise is assumed to be proportional with the yearly sales. It is also assumed that the deviation from the deterministic solution is sufficiently small to make a small noise approximation. This perturbation takes the form of a time dependent Ornstein–Uhlenbeck process. For the variance of the perturbation an exact expression can be given which is needed in order to obtain confidence intervals.
ISSN:2190-5983
2190-5983
DOI:10.1186/s13362-019-0059-6