Levy distribution and long correlation times in supermarket sales
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 Levy distribution of exponent alpha = 1.4, similar to financial exchange markets and in stock markets; and (4) this noise is correlated over a period of 10 to 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.
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- 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.
- Ponzi, A. & Aizawa, Y., 2000. "Evolutionary financial market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 507-523.
- Janssen, Marco A. & Jager, Wander, 2001. "Fashions, habits and changing preferences: Simulation of psychological factors affecting market dynamics," Journal of Economic Psychology, Elsevier, vol. 22(6), pages 745-772, December.
- Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-11, May.
- Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
- Gérard Weisbuch & Dietrich Stauffer, 2000. "Hits and Flops Dynamics," Working Papers 00-07-036, Santa Fe Institute.
- 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.
- 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.
- Damien Challet & Matteo Marsili & Yi-Cheng Zhang, 1999.
"Modeling Market Mechanism with Minority Game,"
- 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.
- 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.
- Weisbuch, Gérard & Stauffer, Dietrich, 2000. "Hits and flops dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 563-576.
- 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.
- 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.
- Rama Cont & Jean-Philippe Bouchaud, 1997. "Herd behavior and aggregate fluctuations in financial markets," Science & Finance (CFM) working paper archive 500028, Science & Finance, Capital Fund Management.
- 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.
- Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(02), pages 170-196, June.
- 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.
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