Boltzmann-Gibbs Entropy to measure Fluctuation of Stock Index
Abstract
The disorder of a physical system can be measured based on the entropy of the system. The greater the entropy value of a system, the more disorder the system increases. In Physics, the disorder of system is measured by Boltzmann-Gibbs Entropy. Boltzmann-Gibbs entropy relates the disorder of a system to the probability distribution of the system's states. The Boltzmann-Gibbs entropy can be extended to more general systems to become the Shanon entropy widely used in information theory. In this research, Boltzmann-Gibbs entropy is used to measure stock market disorder or the fluctuation of stock price. The fluctuation in the stock market are more focused on disorder movements, therefore Boltzman Gibbs entropy is developed into time-dependent entropy using a sliding window technique. The samples in this study were stock indices in Germany (GDAXI), China (HIS), Japan (Nikkei), the United States (Dow-Jones), and Indonesia (IDX). The calculation results show an increase in Boltzman-Gibbs entropy when the economic crisis begins. Entropy decreases when the crisis begins to subside towards a more stable.
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