Hawkes processes for Covid-19 patients of  estimation Parameters

Authors

  • Prof .Dr. Muhannad F. Al-Saadon Faculty of Administration and Economics/University of Al-Qadisiyah
  • Researcher Ayman Abbas najm Faculty of Administration and Economics/University of Al-Qadisiyah

DOI:

https://doi.org/10.36322/jksc.177(A).19019

Keywords:

Hawkes, Self-exciting, Poisson, Counting, Point, Exponential kernel, Conditional intensity, Exponential decay

Abstract

The paper dealt with the study of stochastic self-exciting processes called Hawkes processes, where it is usually many accidents as they occurs form data over time, which are called cluster events. That is, the processes of arrival or the occurrence of the event are represented by the cluster samples in which it is the occurrence of each event stimulates the occurrence of another event at an accelerated rate, similar to a cluster. hence it can be said that Hawkes process are a type of stochastic process that can be categorized into many types of data, it is characterized by the fact that its occurrence is followed by the occurrence of accidents rapidly, such as the occurrence of rebounds after a certain earthquake, or any trading operations in finance market or a stock market after a certain jump in trading.

The aim of this paper is to study the behavior of the Hawkes process using a method to estimate the parameters of the Hawkes process, where the quality criterion bias and standard deviation were used to judge the performance of estimation methods in terms of the quality of estimators using patient data Covid-19.

Downloads

Download data is not yet available.

References

المراجع:

1. Bartlett, M. S. (1963). The spectral analysis of point processes. Journal of the Royal Statistical Society: Series B (Methodological), 25(2), 264-281.

2. Bartlett, M. S. (1964). The spectral analysis of two-dimensional point processes. Biometrika, 51(3/4), 299-311.

3. Bowsher, C. G. (2007). Modelling security market events in continuous time: Intensity based, multivariate point process models. Journal of Econometrics, 141(2), 876-912.

4. Cox, D. R. (1955). Some statistical methods connected with series of events. Journal of the Royal Statistical Society: Series B (Methodological), 17(2), 129-157.

5. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 1-22.

6. Haghdan, M. (2017). Hawkes Process Models for Unsupervised Learning on Uncertain Event Data (Doctoral dissertation, University of Toledo).

7. Hawkes, A. G. (1971). Point spectra of some mutually exciting point processes. Journal of the Royal Statistical Society: Series B (Methodological), 33(3), 438-443.

8. Hawkes, A. G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58(1), 83-90.

9. Laub, P. J., Taimre, T., & Pollett, P. K. (2015). Hawkes processes. arXiv preprint arXiv:1507.02822.

10. Lewis, P. A. (1964). A branching Poisson process model for the analysis of computer failure patterns. Journal of the Royal Statistical Society: Series B (Methodological), 26(3), 398-441.

11. Obral, K. (2016). Simulation, estimation and applications of hawkes processes (Doctoral dissertation, Master’s thesis, University of Minnesota).

12. Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical association, 83(401), 9-27.

13. Olson, J. F., & Carley, K. M. (2013). Exact and approximate em estimation of mutually exciting hawkes processes. Statistical Inference for Stochastic Processes, 16(1), 63-80.

14. Ozaki, T. (1979). Maximum likelihood estimation of Hawkes' self-exciting point processes. Annals of the Institute of Statistical Mathematics, 31(1), 145-155.

15. Rodriguez.A.B.(2019). Hawkes processes in finance. thesis. university of Barcelona. http://diposit.ub.edu.

16. Veen, A., & Schoenberg, F. P. (2008). Estimation of space–time branching process models in seismology using an em–type algorithm. Journal of the American Statistical Association, 103(482), 614-624.

17. Vere-Jones, D. (1978). Earthquake prediction-a statistician's view. Journal of Physics of the Earth, 26(2), 129-146.

18. Wang.Q.(2015).Applications of Hawkes process in Finance.Master thesis. Tilburg University. http://arno.uvt.nl.

Downloads

Published

2026-04-12

How to Cite

Al-Saadon, M. and najm, A. (2026) “Hawkes processes for Covid-19 patients of  estimation Parameters”, Journal of Kufa Studies Center, 1(77(A), pp. 133–150. doi:10.36322/jksc.177(A).19019.

Share