A comparative study of symbolic aggregate approximation and topological data analysis

Fredrik Hobbelhagen; Ioannis Diamantis; Fredrik Hobbelhagen; Ioannis Diamantis

doi:10.3934/QFE.2024027

Quantitative Finance and Economics

2024, Volume 8, Issue 4: 705-732. doi: 10.3934/QFE.2024027

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Research article

A comparative study of symbolic aggregate approximation and topological data analysis

Fredrik Hobbelhagen ,
Ioannis Diamantis ^,

School of Business and Economics, Maastricht University, P.O.BOX 616, 6200 MD, Maastricht, The Netherlands

Received: 06 August 2024 Revised: 08 October 2024 Accepted: 24 October 2024 Published: 30 October 2024
JEL Codes: C63; C65; C53; C18

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.
- topological data analysis,
- symbolic aggregate approximation,
- comparison, time series, stock markets
Citation: Fredrik Hobbelhagen, Ioannis Diamantis. A comparative study of symbolic aggregate approximation and topological data analysis[J]. Quantitative Finance and Economics, 2024, 8(4): 705-732. doi: 10.3934/QFE.2024027

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Abstract

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.

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