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

Hiroshi Ogura (), Yasutaka Hanada, Keitaro Osakabe and Masato Kondo
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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

J, 2025, vol. 8, issue 4, 1-26

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.

Keywords: Hawkes process; autocorrelation function; stochastic process; long-range correlation; word occurrence; maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: I1 I10 I12 I13 I14 I18 I19 (search for similar items in EconPapers)
Date: 2025
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