Detecting Anomalies in the Dynamics of a Market Index with Topological Data Analysis, International Journal of Systematic Innovation
"We investigate the collective behavior of a stock market by studying the dynamics of its representative index’s return, using the persistence diagram of the index return’s time-delay embedding, an approach of the Topological Data Analysis (TDA) in time series analysis. While the time-delay emb...
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| Tác giả chính: | , |
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| Định dạng: | text::journal::journal article |
| Ngôn ngữ: | en_US |
| Thông tin xuất bản: |
2022
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| Chủ đề: | |
| Truy cập trực tuyến: | http://repository.vlu.edu.vn:443/handle/123456789/292 |
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| Tóm tắt: | "We investigate the collective behavior of a stock market by studying the dynamics of its representative index’s
return, using the persistence diagram of the index return’s time-delay embedding, an approach of the
Topological Data Analysis (TDA) in time series analysis. While the time-delay embedding captures the state
space of the index return’s dynamics, the persistence diagram encodes the space's topological information under
different spatial resolu-tions. Therefore, based on the changes in the point distribution of the persistence diagram
over time, we propose a framework to detect its extraordinary movements. Our method provides a measure for
the stability level of the mar-ket’s collective behavior. After applying this method for the daily return of the S&P
500 index from 1970 to 2020, we demonstrate that the measure efficiently tracks the changes in topological
information of the index re-turn. Furthermore, we can capture major American recessions when the measure
exceeds a threshold. A continuous and rapid increase of the measure approaching the threshold is considered a
warning of a crisis. Hence, our method provides a technical indicator for systematic risk management." |
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