Symbolic Encoding Methods with Entropy-Based Applications to Financial Time Series Analyses

Abstract

Symbolic encoding of information is the foundation of Shannon’s mathematical theory of communication. The concept of the informational efficiency of capital markets is closely related to the issue of information processing by equity market participants. Therefore, the aim of this comprehensive research is to examine and compare a battery of methods based on symbolic coding with thresholds and the modified Shannon entropy in the context of stock market efficiency. As these methods are especially useful in assessing the market efficiency in terms of sequential regularity in financial time series during extreme events, two turbulent periods are analyzed: (1) the COVID-19 pandemic outbreak and (2) the period of war in Ukraine. Selected European equity markets are investigated. The findings of empirical experiments document that the encoding method with two 5% and 95% quantile thresholds seems to be the most effective and precise procedure in recognizing the dynamic patterns in time series of stock market indices. Moreover, the Shannon entropy results obtained with the use of this symbolic encoding method are homogenous for all investigated markets and unambiguously confirm that the market informational efficiency measured by the entropy of index returns decreases during extreme event periods. Therefore, we can recommend the use of this STSA method for financial time series analyses.

Keywords

• symbolic time series analysis (STSA)
• symbol–sequence histogram
• modified Shannon entropy
• stock market
• informational efficiency
• extreme event