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Modeling the Mutual Dynamic Correlations of Words in Written Texts Using Multivariate Hawkes Processes

Author

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  • Hiroshi Ogura

    (Faculty of Arts and Sciences at FUJIYOSHIDA, Showa Medical University, 4562 Kamiyoshida, Fujiyoshida-shi 403-0005, Japan)

  • Yasutaka Hanada

    (Faculty of Arts and Sciences at FUJIYOSHIDA, Showa Medical University, 4562 Kamiyoshida, Fujiyoshida-shi 403-0005, Japan)

  • Keitaro Osakabe

    (Faculty of Arts and Sciences at FUJIYOSHIDA, Showa Medical University, 4562 Kamiyoshida, Fujiyoshida-shi 403-0005, Japan)

  • Masato Kondo

    (Faculty of Arts and Sciences at FUJIYOSHIDA, Showa Medical University, 4562 Kamiyoshida, Fujiyoshida-shi 403-0005, Japan)

Abstract

The occurrence patterns of important words found in six texts (one historical pamphlet and five renowned academic books) are analyzed using both univariate and multivariate Hawkes processes. By treating the occurrence patterns as binary time-series data along the texts, we investigate how effectively univariate and multivariate Hawkes processes capture the characteristics of these word occurrence signals. Through maximum likelihood estimation and subsequent simulations, we found that the multivariate Hawkes process clearly outperforms the univariate Hawkes process in modeling word occurrence signals. Moreover, we found that the multivariate Hawkes process can provide a Hawkes graph, which serves as an intuitive representation of the relationships between concepts appearing in the analyzed text. Furthermore, our study demonstrates that the importance of concepts within a given text can be quantitatively estimated based on the optimized parameter values of the multivariate Hawkes process.

Suggested Citation

  • Hiroshi Ogura & Yasutaka Hanada & Keitaro Osakabe & Masato Kondo, 2025. "Modeling the Mutual Dynamic Correlations of Words in Written Texts Using Multivariate Hawkes Processes," J, MDPI, vol. 8(4), pages 1-26, October.
    • Handle: RePEc:gam:jjopen:v:8:y:2025:i:4:p:40-:d:1770519
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    References listed on IDEAS

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    1. Chatzigeorgiou, M. & Constantoudis, V. & Diakonos, F. & Karamanos, K. & Papadimitriou, C. & Kalimeri, M. & Papageorgiou, H., 2017. "Multifractal correlations in natural language written texts: Effects of language family and long word statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 173-182.
    2. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    3. Steve Y. Yang & Anqi Liu & Jing Chen & Alan Hawkes, 2018. "Applications of a multivariate Hawkes process to joint modeling of sentiment and market return events," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 295-310, February.
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