# Maximum Entropy Principle underlying the dynamics of automobile sales

## TL;DR

This study analyzes 10 years of Spanish car sales data, revealing that high-market-share models follow proportional growth dynamics and that total sales distribution aligns with the Maximum Entropy Principle, with sales being predictable over several years.

## Contribution

It demonstrates that car sales dynamics adhere to the Maximum Entropy Principle and Gibrat's law, introducing a Langevin equation-based model capturing non-Markovian effects and predictability.

## Key findings

- Sales follow Gibrat's law for models with >0.1% market share.
- Total sales distribution matches Maximum Entropy predictions.
- Sales dynamics exhibit a 5-year memory effect.

## Abstract

We analyze an exhaustive data-set of new-cars monthly sales. The set refers to 10 years of Spanish sales of more than 6500 different car model configurations and a total of 10M sold cars, from January 2007 to January 2017. We find that for those model configurations with a monthly market-share higher than 0.1% the sales become scalable obeying Gibrat's law of proportional growth under logistic dynamics. Remarkably, the distribution of total sales follows the predictions of the Maximum Entropy Principle for systems subject to proportional growth in dynamical equilibrium. We also encounter that the associated dynamics are non-Markovian, i.e., the system has a decaying memory or inertia of about 5 years. Thus, car sales are predictable within a certain time-period. We show that the main characteristics of the dynamics can be described via a construct based upon the Langevin equation. This construct encompasses the fundamental principles that any predictive model on car sales should obey.