Permutation Entropy as a Measure of Information Gain/Loss in the Different Symbolic Descriptions of Financial Data

Financial markets give a large number of trading opportunities. However, over-complicated systems make it very difficult to be effectively used by decision-makers. Volatility and noise present in the markets evoke a need to simplify the market picture derived for the decision-makers. Symbolic representation fits in this concept and greatly reduces data complexity. However, at the same time, some information from the market is lost. Our motivation is to answer the question: What is the impact of introducing different data representation on the overall amount of information derived for the decision-maker? We concentrate on the possibility of using entropy as a measure of the information gain/loss for the financial data, and as a basic form, we assume permutation entropy with later modifications. We investigate different symbolic representations and compare them with classical data representation in terms of entropy. The real-world data covering the time span of 10 years are used in the experiments. The results and the statistical verification show that extending the symbolic description of the time series does not affect the permutation entropy values.