IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v353y2005icp501-514.html
   My bibliography  Save this article

Lévy distribution and long correlation times in supermarket sales

Author

Listed:
  • Groot, Robert D.

Abstract

Sales data in a commodity market (supermarket sales to consumers) has been analysed by studying the fluctuation spectrum and noise correlations. Three related products (ketchup, mayonnaise and curry sauce) have been analysed. Most noise in sales is caused by promotions, but here we focus on the fluctuations in baseline sales. These characterise the dynamics of the market. Four hitherto unnoticed effects have been found that are difficult to explain from simple econometric models. These effects are: (1) the noise level in baseline sales is much higher than can be expected for uncorrelated sales events; (2) weekly baseline sales differences are distributed according to a broad non-Gaussian function with fat tails; (3) these fluctuations follow a Lévy distribution of exponent α=1.4, similar to financial exchange markets and in stock markets; and (4) this noise is correlated over a period of 10–11 weeks, or shows an apparent power law spectrum. The similarity to stock markets suggests that models developed to describe these markets may be applied to describe the collective behaviour of consumers.

Suggested Citation

  • Groot, Robert D., 2005. "Lévy distribution and long correlation times in supermarket sales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 501-514.
    • Handle: RePEc:eee:phsmap:v:353:y:2005:i:c:p:501-514
    DOI: 10.1016/j.physa.2004.12.064
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104016085
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2004.12.064?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
    2. E. Ahmed & H.A. Abdusalam, 2000. "On social percolation and small world network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 16(3), pages 569-571, August.
    3. W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
    4. Sornette, D & Helmstetter, A, 2003. "Endogenous versus exogenous shocks in systems with memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 577-591.
    5. Stanley, H.Eugene, 2003. "Statistical physics and economic fluctuations: do outliers exist?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(1), pages 279-292.
    6. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(2), pages 170-196, June.
    7. Bak, Per, 1992. "Self-organized criticality in non-conservative models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 41-46.
    8. Solomon, Sorin & Weisbuch, Gerard & de Arcangelis, Lucilla & Jan, Naeem & Stauffer, Dietrich, 2000. "Social percolation models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 239-247.
    9. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
    10. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    11. Goldenberg, J & Libai, B & Solomon, S & Jan, N & Stauffer, D, 2000. "Marketing percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 335-347.
    12. Challet, Damien & Marsili, Matteo & Zhang, Yi-Cheng, 2000. "Modeling market mechanism with minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 276(1), pages 284-315.
    13. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    14. Weisbuch, Gérard & Stauffer, Dietrich, 2000. "Hits and flops dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 563-576.
    15. Castiglione, F & Pandey, R.B & Stauffer, D, 2001. "Effect of trading momentum and price resistance on stock market dynamics: a Glauber Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 223-228.
    16. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    17. da Silva, L.R & Stauffer, D, 2001. "Ising-correlated clusters in the Cont-Bouchaud stock market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(1), pages 235-238.
    18. Ponzi, A. & Aizawa, Y., 2000. "Evolutionary financial market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 507-523.
    19. Gérard Weisbuch & Dietrich Stauffer, 2000. "Hits and Flops Dynamics," Working Papers 00-07-036, Santa Fe Institute.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. R. D. Groot, 2004. "Levy distribution and long correlation times in supermarket sales," Papers cond-mat/0412163, arXiv.org.
    2. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    3. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    4. Gu, Gao-Feng & Chen, Wei & Zhou, Wei-Xing, 2008. "Empirical regularities of order placement in the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3173-3182.
    5. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    6. Gao-Feng Gu & Xiong Xiong & Hai-Chuan Xu & Wei Zhang & Yongjie Zhang & Wei Chen & Wei-Xing Zhou, 2021. "An empirical behavioral order-driven model with price limit rules," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-24, December.
    7. Sornette, Didier & Zhou, Wei-Xing, 2006. "Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 704-726.
    8. Fibich, Gadi & Levin, Tomer, 2020. "Percolation of new products," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    9. Johann Lussange & Ivan Lazarevich & Sacha Bourgeois-Gironde & Stefano Palminteri & Boris Gutkin, 2021. "Modelling Stock Markets by Multi-agent Reinforcement Learning," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 113-147, January.
    10. Rothenstein, R & Pawelzik, K, 2003. "Evolution and anti-evolution in a minimal stock market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 326(3), pages 534-543.
    11. Cross, Rod & Grinfeld, Michael & Lamba, Harbir & Seaman, Tim, 2005. "A threshold model of investor psychology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 463-478.
    12. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    13. Lei Tan & Bo Zheng & Jun-Jie Chen & Xiong-Fei Jiang, 2015. "How Volatilities Nonlocal in Time Affect the Price Dynamics in Complex Financial Systems," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-16, February.
    14. Sun-Chong Wang & Sai-Ping Li & Chung-Ching Tai & Shu-Heng Che, 2009. "Statistical properties of an experimental political futures market," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 9-16.
    15. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    16. Fang, Wen & Ke, Jinchuan & Wang, Jun & Feng, Ling, 2016. "Linking market interaction intensity of 3D Ising type financial model with market volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 531-542.
    17. Katahira, Kei & Chen, Yu & Hashimoto, Gaku & Okuda, Hiroshi, 2019. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 503-518.
    18. Sebastiano A. Delre & Wander Jager & Marco A. Janssen, 2007. "Diffusion dynamics in small-world networks with heterogeneous consumers," Computational and Mathematical Organization Theory, Springer, vol. 13(2), pages 185-202, June.
    19. Kaizoji, Taisei & Miyano, Michiko, 2016. "Why does the power law for stock price hold?," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 19-23.
    20. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.

    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:eee:phsmap:v:353:y:2005:i:c:p:501-514. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.