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Forecasting New Product Diffusion Using Grey Time‐Delayed Verhulst Model

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  • Yuhong Wang
  • Shulin Yang
  • Wuyong Qian
  • Xiaozhong Li

Abstract

Taking account of the time‐delayed phenomenon in diffusion of new products, we propose the time‐delayed Verhulst model and then establish a grey time‐delayed Verhulst model using the method of grey differential equations. The related parameter packets of this novel model are obtained under the rule of ordinary least squares (OLS). The results show that the traditional grey Verhulst model is a special example of grey time‐delayed Verhulst model which can reflect the time‐delayed information effectively. A practical example of market diffusion shows that the modeling accuracy is remarkably improved by using the grey time‐delayed Verhulst model presented in this paper.

Suggested Citation

  • Yuhong Wang & Shulin Yang & Wuyong Qian & Xiaozhong Li, 2013. "Forecasting New Product Diffusion Using Grey Time‐Delayed Verhulst Model," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:625028
    DOI: 10.1155/2013/625028
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    References listed on IDEAS

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    1. Pao, Hsiao-Tien & Fu, Hsin-Chia & Tseng, Cheng-Lung, 2012. "Forecasting of CO2 emissions, energy consumption and economic growth in China using an improved grey model," Energy, Elsevier, vol. 40(1), pages 400-409.
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    Cited by:

    1. Zhineng Hu & Yurong Pei & Ruikun Xie, 2014. "Analysis of Product Sampling for New Product Diffusion Incorporating Multiple‐Unit Ownership," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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