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Unveiling complex nonlinear dynamics in stock markets through topological data analysis

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  • Nie, Chun-Xiao

Abstract

Testing and characterizing nonlinear serial dependence in financial time series constitutes a critical research focus, extensively applied in examining weak-form market efficiency. This study demonstrates ATCC’s capability to capture nonlinear dependence and employs it to analyze equity market return series. Our findings reveal that rolling-window ATCC can characterize high-resolution dynamics of dependence. For instance, using minute-level data, we document how the Russia–Ukraine conflict information significantly impacted dependence structures in the Chinese market. Furthermore, based on daily index data, the 2025 Trump tariff policies are shown to have substantially influenced dependence patterns in both Chinese and U.S. market indices. Notably, through combined ATCC and linear modeling of SSE 50 constituent returns, we find that while linear models adequately characterize dependence in most daily returns, a minority of stocks exhibit nonlinear serial dependence. This research establishes an ATCC-based analytical framework, providing an effective quantitative tool for investigating nonlinear serial dependence and its high-resolution dynamics.

Suggested Citation

  • Nie, Chun-Xiao, 2025. "Unveiling complex nonlinear dynamics in stock markets through topological data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 680(C).
    • Handle: RePEc:eee:phsmap:v:680:y:2025:i:c:s0378437125006776
    DOI: 10.1016/j.physa.2025.131025
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    1. McKenzie, Michael D. & Faff, Robert W., 2005. "Modeling conditional return autocorrelation," International Review of Financial Analysis, Elsevier, vol. 14(1), pages 23-42.
    2. Claudio Bonilla & Rafael Romero-Meza & Melvin Hinich, 2006. "Episodic nonlinearity in Latin American stock market indices," Applied Economics Letters, Taylor & Francis Journals, vol. 13(3), pages 195-199.
    3. Robert W. Faff & Michael D. McKenzie, 2007. "The relationship between implied volatility and autocorrelation," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 3(2), pages 191-196, April.
    4. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    5. Andrew Urquhart, 2014. "The Euro and European stock market efficiency," Applied Financial Economics, Taylor & Francis Journals, vol. 24(19), pages 1235-1248, October.
    6. Kian-Ping Lim & Chee-Wooi Hooy, 2013. "Non-Linear Predictability In G7 Stock Index Returns," Manchester School, University of Manchester, vol. 81(4), pages 620-637, July.
    7. Hinich, Melvin J & Patterson, Douglas M, 1985. "Evidence of Nonlinearity in Daily Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(1), pages 69-77, January.
    8. Robert W. Faff & Michael D. McKenzie, 2007. "The relationship between implied volatility and autocorrelation," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 3(2), pages 191-196, April.
    9. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2011. "Small sample properties of alternative tests for martingale difference hypothesis," Economics Letters, Elsevier, vol. 110(2), pages 151-154, February.
    10. McKenzie, Michael D. & Kim, Suk-Joong, 2007. "Evidence of an asymmetry in the relationship between volatility and autocorrelation," International Review of Financial Analysis, Elsevier, vol. 16(1), pages 22-40.
    11. Robert W. Faff & Michael D. McKenzie, 2007. "The relationship between implied volatility and autocorrelation," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 3(2), pages 191-196, April.
    12. Choi, In, 1999. "Testing the Random Walk Hypothesis for Real Exchange Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 293-308, May-June.
    13. Ito, Mikio & Sugiyama, Shunsuke, 2009. "Measuring the degree of time varying market inefficiency," Economics Letters, Elsevier, vol. 103(1), pages 62-64, April.
    14. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    15. Dong, Xi & Feng, Shu & Ling, Leng & Song, Pingping, 2017. "Dynamic autocorrelation of intraday stock returns," Finance Research Letters, Elsevier, vol. 20(C), pages 274-280.
    16. Urquhart, Andrew & McGroarty, Frank, 2016. "Are stock markets really efficient? Evidence of the adaptive market hypothesis," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 39-49.
    17. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    18. Katz, Yuri A. & Biem, Alain, 2021. "Time-resolved topological data analysis of market instabilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    19. Kian-Ping Lim & Weiwei Luo & Jae H. Kim, 2013. "Are US stock index returns predictable? Evidence from automatic autocorrelation-based tests," Applied Economics, Taylor & Francis Journals, vol. 45(8), pages 953-962, March.
    20. Rafael Romero-Meza & Claudio Bonilla & Melvin Hinich, 2007. "Nonlinear event detection in the Chilean stock market," Applied Economics Letters, Taylor & Francis Journals, vol. 14(13), pages 987-991.
    21. Kian‐Ping Lim & Robert Brooks, 2011. "The Evolution Of Stock Market Efficiency Over Time: A Survey Of The Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 69-108, February.
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