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Lévy distribution and long correlation times in supermarket sales

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  • 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
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    1. 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.
    2. 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.
    3. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
    10. 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.
    11. 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.
    12. Bak, Per, 1992. "Self-organized criticality in non-conservative models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 41-46.
    13. 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.
    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.
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