The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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An overview of Hawkes processes and their applications

혹스 과정의 개요 및 응용

  • Mijeong Kim (Department of Statistics, Ewha Womans University)
  • 김미정 (이화여자대학교 통계학과)
  • Received : 2023.02.01
  • Accepted : 2023.03.13
  • Published : 2023.08.31
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Abstract

The Hawkes process is a point process with self-exciting characteristics. It has been mainly used to describe seismic phenomena in which aftershocks occur due to the main earthquake. Recently, it has been used to explain various phenomena with self-exciting properties, such as the spread of infectious diseases and the spread of news on SNS. The Hawkes process can be flexibly modified according to the characteristics of events by using various types of excitation functions. Since it is difficult to implement a maximum likelihood estimator numerically, estimation methods have been improved until recently. In this paper, the conditional intensity function and excitation function are explained to describe the Hawkes process. Then, existing examples of Hawkes processes used in seismic, epidemiological, criminal, and financial fields are described and estimation methods are introduced. I analyze earthquakes that occurred in gyeongsang-do, Korea from November 2017 to December 2022, using R package ETAS.

혹스 과정은 자기 자극 특성을 가진 점 과정으로서, 지진 발생시 본진으로 인한 여진이 발생되는 현상을 설명하는 데 주로 쓰이는 확률 모형이다. 최근에는 전염병 확산, SNS에서의 소식 확산 등 자기 자극을 특성을 가진 다양한 현상을 설명하는 데 활용되고 있다. 혹스 과정은 다양한 형태의 자극 함수를 도입하여 발생하는 사건의 특성에 따라 유연하게 변형이 가능한데, 최대 우도 추정량을 구하는 것이 쉽지 않기 때문에 최근까지도 개선된 추정 방법이 제시되고 있다. 이 논문에서는 혹스 과정을 설명하기 위해 조건부 강도 함수와 자극 함수에 대해 설명하고, 지진, 전염병, 범죄 및 금융에서 활용되었던 예와 추정 방법을 알아보도록 한다. R-패키지 ETAS를 이용하여 2017년 11월부터 2022년 12월까지 한국 경상도에서 발생한 지진을 분석하도록 한다.

Keywords

Acknowledgement

이 논문은 연구재단 연구 과제 NRF-2020R1F1A1A01074157에 의하여 수행되었음.

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