IDEAS home Printed from https://ideas.repec.org/p/toh/tmarga/113.html
   My bibliography  Save this paper

Multivariate Time Series Model with Hierarchical Structure for Over-dispersed Discrete Outcomes

Author

Listed:
  • Nobuhiko Terui
  • Masataka Ban

Abstract

In this paper, we propose a multivariate time series model for over-dispersed discrete data to explore the market structure based on sales count dynamics. We first discuss the microstructure to show that over-dispersion is inherent in the modeling of market structure based on sales count data. The model is built on the likelihood function induced by decomposing sales count response variables according to products' competitiveness and conditioning on their sum of variables, and it augments them to higher levels by using Poisson-Multinomial relationship in a hierarchical way, represented as a tree structure for the market definition. State space priors are applied to the structured likelihood to develop dynamic generalized linear models for discrete outcomes. For over-dispersion problem, Gamma compound Poisson variables for product sales counts and Dirichlet compound multinomial variables for their shares are connected in a hierarchical fashion. Instead of the density function of compound distributions, we propose a data augmentation approach for more efficient posterior computations in terms of the generated augmented variables particularly for generating forecasts and predictive density. We present the empirical application using weekly product sales time series in a store to compare the proposed models accommodating over-dispersion with alternative no over-dispersed models by several model selection criteria, including in-sample fit, out-of-sample forecasting errors, and information criterion. The empirical results show that the proposed modeling works well for the over-dispersed models based on compound Poisson variables and they provide improved results than models with no consideration of over-dispersion.

Suggested Citation

  • Nobuhiko Terui & Masataka Ban, 2013. "Multivariate Time Series Model with Hierarchical Structure for Over-dispersed Discrete Outcomes," TMARG Discussion Papers 113, Graduate School of Economics and Management, Tohoku University, revised Aug 2013.
  • Handle: RePEc:toh:tmarga:113
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10097/56551
    Download Restriction: no

    References listed on IDEAS

    as
    1. Nobuhiko Terui & Masataka Ban & Toshihiko Maki, 2010. "Finding market structure by sales count dynamics—Multivariate structural time series models with hierarchical structure for count data—," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 91-107, February.
    2. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-417, October.
    3. Bearden, William O & Etzel, Michael J, 1982. " Reference Group Influence on Product and Brand Purchase Decisions," Journal of Consumer Research, Oxford University Press, vol. 9(2), pages 183-194, September.
    4. Park, C Whan & Lessig, V Parker, 1977. " Students and Housewives: Differences in Susceptibility to Reference Group Influence," Journal of Consumer Research, Oxford University Press, vol. 4(2), pages 102-110, Se.
    5. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:toh:tmarga:113. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tohoku University Library). General contact details of provider: http://edirc.repec.org/data/fetohjp.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.