A comparative study of symbolic aggregate approximation and topological data analysis

The movement of stocks is often perceived as random due to the complex interactions between different stocks and the inherently chaotic nature of the market. This study investigated the similarity in stock movements across multiple industry sectors in Europe. Specifically, we applied topological data analysis (TDA) to analyze stock time series data and compared the results with those obtained using an expanded form of a more classical time series analysis method, symbolic aggregate approximation (SAX). Our findings indicated that while TDA offered detailed insights into "local" stock movements, SAX was more effective in capturing broader trends in financial markets, where less detail was required, making it suitable for portfolio optimization. We also presented an extension of SAX that incorporated volatility measures, improving its performance in highly volatile markets.