Forecasting product sales with a stochastic Bass model

Johan Grasman*, Marcel Kornelis

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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.

Original languageEnglish
Article number2
Number of pages10
JournalJournal of Mathematics in Industry
Volume9
DOIs
Publication statusPublished - 7 Feb 2019

Fingerprint

Stochastic models
Confidence interval
Forecasting
Sales
Perturbation
Point Estimate
Deviation
Directly proportional
Interval
Term
Approximation
Model
Estimate
Form

Keywords

  • Bass model
  • Confidence domain
  • Ornstein–Uhlenbeck process
  • Sensitivity of parameter to data

Cite this

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Forecasting product sales with a stochastic Bass model. / Grasman, Johan; Kornelis, Marcel.

In: Journal of Mathematics in Industry, Vol. 9, 2, 07.02.2019.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Forecasting product sales with a stochastic Bass model

AU - Grasman, Johan

AU - Kornelis, Marcel

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AB - 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.

KW - Bass model

KW - Confidence domain

KW - Ornstein–Uhlenbeck process

KW - Sensitivity of parameter to data

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DO - 10.1186/s13362-019-0059-6

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