Levy distribution and long correlation times in supermarket sales

TL;DR

This paper reveals that supermarket baseline sales fluctuations follow a Levy distribution with long-range correlations, similar to financial markets, indicating complex collective consumer behavior not explained by simple models.

Contribution

It uncovers four new effects in supermarket sales data, including Levy-distributed fluctuations and long correlation times, challenging traditional econometric assumptions.

Findings

Noise in baseline sales exceeds uncorrelated expectations

Fluctuations follow a Levy distribution with alpha=1.4

Correlations persist over 10-11 weeks, showing power law spectrum

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 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.