Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 123-143 (2021)

A Personal History of Hawkes Processes

Alan Hawkes
(School of Management, Swansea University)
Jing Chen
(School of Mathematics, Cardiff University)

This paper is based on an interview with Alan Hawkes about the series of five papers published 1971–1974 on self-exciting and mutually-exciting point processes that came to be known as Hawkes processes. This is supplemented by additional material describing the background before the papers were published, why it was 40 years before he returned to the subject of Hawkes processes and some of the things that have since been achieved.

Key words: Queue, ETAS model, ion-channel, reliability, finance, stochastic process.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 145-163 (2021)

The ETAS Model in Statistical Seismology: Its History, Recent Developments, and Influences on General Hawkes Processes

Jiancang Zhuang
(The Institute of Statistical Mathematics)
Yosihiko Ogata
(The Institute of Statistical Mathematics, Professor Emeritus)

We review the history of the ETAS model, a model for standard seismicity, in statistical seismology. In addition, we review new developments in theory, methods, and applications of the model, as well as its influences on the developments of general Hawkes processes.

Key words: ETAS model, Hawkes process, statistical seismology, point processes.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 165-180 (2021)

Hawkes-type Count Time Series Models

Shinsuke Koyama
(The Institute of Statistical Mathematics)

We propose a "Hawkes-type" count time series model. By emphasizing the branching process representation of the Hawkes process on a real number line, our model has a similar representation. The applicability of the proposed model is demonstrated using an epidemiological example where the effective reproduction number proposed by Wallinga and Teunis (2004) is generalized for over-dispersion.

Key words: Hawkes process, branching process, count time series model, negative binomial distribution, effective reproduction number.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 181-207 (2021)

Comparison of Two Estimation Methods for Hawkes Processes and Application to Actual Data Analysis

Shuji Chinone
(Graduate School of Science and Technology, Keio University)
Hiroshi Shiraishi
(Faculty of Science and Technology, Keio University)

We consider multivariate Hawkes processes that are a class of multivariate point processes with self and mutual excitation properties. In this paper, we assume that the observed data follow a multivariate Hawkes process, and consider two statistical estimation methods of the kernel function, which represents the characteristics of the Hawkes process. The first method is a parametric approach using the maximum likelihood method. It estimates the parameters of the kernel function on the assumption that the intensity dependency follows the exponential kernel function. The second method is a non-parametric approach that does not specify the kernel function. The kernel function is estimated non-parametrically by approximating the continuous-time stochastic process based on discrete observation. After comparing the estimation results of the two methods using simulation, we fit the price and volume fluctuations in the cryptocurrency market to the Hawkes process based on the param etric approach, and visualize the propagation structure through the Hawkes graph representation, which is a method for visualizing the characteristics of kernel functions. Furthermore, the number of people in the Kanto and Kansai regions in Japan who were newly infected COVID-19 is fitted to the Hawkes process based on the non-parametric approach, and the propagation structure is seen by the Hawkes graph representation.

Key words: Hawkes process, multivariate point process, INAR process, Hawkes graph, graphical modeling, non-parametric estimation.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 209-222 (2021)

A Nonlinear Hawkes Process in Seismology: A Seismicity Model Based on Rate- and State-dependent Friction Law

Takaki Iwata
(Comprehensive Education Center, Prefectural University of Hiroshima/The Institute of Statistical Mathematics)

This review introduces the Dieterich model, which is a seismicity model based on rate- and state-dependent friction law. Herein the Dieterich model is compared to the epidemic-type aftershock sequence (ETAS) model, which is the best-known model for seismicity analysis. The Dieterich model is a nonlinear Hawkes process, while ETAS is a linear Hawkes process. This review also presents other contrastive characteristics between the two models. Additionally, the advantages and disadvantages of the Dieterich model along with future directions are discussed.

Key words: Seismicity, nonlinear Hawkes process, rate- and state-dependent friction law, point-process analysis, stress, Dieterich model.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 223-237 (2021)

Extended Versions of the Space-time ETAS Model and Their Applications

Yicun Guo
(Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences)
Jiancang Zhuang
(The Institute of Statistical Mathematics/Department of Statistical Science, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies (SOKENDAI))

This paper summarizes several extended versions of the space-time Epidemic-type Aftershock Sequence (ETAS) model. The ETAS model is commonly accepted as a standard model in statistical seismology, and its extended versions include the 2D finite source (FS) model, the 3D hypocentral model, and the 3D-FS model. The finite source model incorporates the rupture geometries of large earthquakes, while the 3D hypocentral model considers focal depths of earthquakes. The relevant algorithms for model estimation, stochastic declustering, and earthquake simulations are given. Additionally, the results from previous applications of the finite source and 3D ETAS models to Japan, Italy, and Southern California are summarized. The 2D-FS and 3D-FS models enhance the productivity of mainshocks by yielding a larger α value than the point source model. Comparing the aftershock productivity with the coseismic slip suggests that large slip areas are depleted of aftershocks, and the traje ctory of the productivity pattern on the fault plane demonstrates the apparent compensation to the slip.

Key words: ETAS model, probability density, residual analysis, earthquake triggering, aftershock, stochastic reconstruction.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 239-254 (2021)

Forecasting Repeating Earthquakes Considering Aftershock-triggering Effects

Shunichi Nomura
(Faculty of Commerce, Graduate School of Accountancy, Waseda University)
Masayuki Tanaka
(Department of Seismology and Tsunami Research, Meteorological Research Institute)

Point process models to predict earthquake occurrences (other than the simplest Poisson processes) can be roughly classified into two types: the renewal process for earthquakes repeating periodically on the same hypocenter, such as active faults; and the ETAS (epidemic-type aftershock sequence) model, which takes the aftershock-triggering effect of every earthquake into account. However, relatively small repeating earthquakes have the characteristics of both models: they usually recur periodically, but have very short recurrence intervals after large earthquakes nearby. In this paper, we propose a nonstationary renewal process model for such repeating earthquakes that incorporates the aftershock-triggering effect of nearby large earthquakes as a relative change in the loading rate. We apply the proposed model to the repeating earthquake catalog on the Pacific Plate subduction zone in the northeastern Japan and evaluate probabilistic forecasts of the next repeating events, considering the aftershock-triggering effect of the 2011 Tohoku earthquake.

Key words: Recurrent earthquakes, long-term forecast, Brownian Passage Time distribution, renewal processes, ETAS model.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 259-281 (2021)

Japanese National Character Survey to Cross-national Comparative Survey—From "Statistical Mathematics" to "Science of Data"

Ryozo Yoshino
(Faculty of Culture and Information Science, Doshisha University/The Institute of Statistical Mathematics, Professor Emeritus)

This paper provides an overview of the social situations and world affairs behind the survey research at the Institute of Statistical Mathematics after World War II. In developing a cross-national comparative paradigm called "Cultural Manifold Analysis," the survey team has accumulated not only the results of the data analysis, but also the relevant important information obtained during the course of surveys.
In particular, we recognize that each country's social survey infrastructure itself reflects many important aspects of the social, political, economic, historical and cultural foundations of the country and its people.
We would like to express our sincere gratitude to many collaborators in Japan and overseas for their great support over the past 60 years.

Key words: Asia-Pacific values survey, cross-national survey, Cultural Manifold Analysis, Japanese national character survey, statistical random sampling survey.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 283-294 (2021)

Nonresponse-adjusted Estimates of Population Proportions in the 13th and 14th Nationwide Surveys on the Japanese National Character

Tadayoshi Fushiki
(Faculty of Education, Niigata University)

Nonresponse rates have increased in recent sample surveys in many countries. Since the response rates in the 13th and 14th "Surveys on the Japanese National Character" were about 50%, nonresponse bias is a serious concern. In this study, two nonresponse weighting adjustment methods are used to estimate population proportions based on the 13th and 14th "Surveys on the Japanese National Character." The results showed that estimates of the proportion of people who seek monetary reward, do not trust others, and are not involved with others were increased by bias adjustment. The tendency of bias-adjusted estimates in the 14th survey was relatively consistent with that in the 13th survey.

Key words: Calibration estimation, nonresponse, bias adjustment.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 295-314 (2021)

Environmental Awareness of Japanese Citizens: Quantitative Analysis of Chronological Changes and Related Factors Performed Using the Japanese National Character Survey

Naoko Kato-Nitta
(Joint Support-Center for Data Science Research, Research Organization of Information and Systems)

This paper statistically explored Japanese people's environmental awareness using nationally representative social survey data from the Japanese National Character Survey. It focused on two topics: recent trends in the distribution of the answers to the items assessing environmental awareness, and the determinants of current environmental awareness in Japanese people. For these purposes, analysis was performed using six data series beginning with the 9th Japanese National Character Survey, conducted in 1993, and ending with the 14th Japanese National Character Survey, conducted in 2018 in the Heisei Period. The results revealed that there has been an overall downward trend in environmental awareness in Japan in recent years. This is in contrast with global trends, especially in Europe, which demonstrate a recent increase in people's environmental awareness. Logistic regression analyses of the 14th (2018) data (n=1,602) revealed that the younger generation, especially individuals in their 20s, showed relatively lower environmental awareness. This finding is the opposite of the results of previous studies in some western countries. Highly educated people and those who perceived themselves as being in a higher social class tended to have higher environmental awareness, which was consistent with previous studies in some western countries. Political orientation was also associated with many items, but the results were less clear than those in previous studies in the United States, Europe, or Hong Kong that indicated a strong relationship between environmental awareness and support of liberal parties. This may be because Japan currently lacks explicitly environmental political parties, and because political independents are predominant (56.2%). Further research is needed to confirm these findings.

Key words: Environmental awareness, Japanese National Character Survey, view of nature, energy and economy, political orientation.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 315-337 (2021)

What Factors Determine the Intent to Out-migrate from Urban Areas to Rural Areas? Focusing on the Sense of "Giri ninjō" (Humanity) in the Survey on the Japanese National Character

Yoosung Park
(The Institute of Statistical Mathematics)

Since rural areas in Japan face challenges such as aging populations, abandoned houses, and out-migration, particularly of young people, local governments in many depopulated areas have been promoting several positive rural life activities and experiences, subsidies for housing, and employment support for migrants to rural areas. Previous studies have focused on the effectiveness of maintaining personal community networks, but these networks are subjective and comprise surrounding environments such as limited interpersonal relationships. Therefore, this article focuses on the sense of "Giri ninjō" (humanity), a Japanese psychological mechanism, to clarify the intent to out-migrate from urban areas to rural areas. The sense of "Giri ninjō" has long been accepted as a peculiar characteristic of Japanese interpersonal relationships.
This study seeks to evaluate the intent to out-migrate from urban areas to rural areas in Japan and South Korea, both of which are experiencing a rapid decline in population. According to an analysis using the data of "the Survey on the Japanese National Character" and the "Korean General Social Survey," the groups most likely to out-migrate from urban areas to rural areas are young and middle-aged people in Japan, and middle-aged and older people in South Korea.
This study also aims to explore the relationship between the sense of "Giri ninjō" and the intent to out-migrate from urban areas to rural areas in terms of Japanese attitudes. We conducted logistic regression analysis using the data of "the Survey on the Japanese National Character." The main findings were as follows: (a) the sense of "Giri ninjō" had a positive effect on an intent to out-migrate from urban areas to rural areas; (b) this intent was affected byhigh ability to access information regarding frequent use of the Internet; and (c) the lower perceived positive feelings about the current state of Japanese society derived from the feeling of attachment to the country, the higher intent to out-migrate from urban areas to rural areas.

Key words: The Survey on the Japanese National Character, intent to out-migrate from urban areas to rural areas, sense of "Giri ninjō" (humanity), "Korean General Social Survey", feeling of attachment to the country.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 339-365 (2021)

Methodical Examination on Question Items Measuring Japanese Religious Consciousness/Religiosity: Secondary Analysis of the Japanese National Character Survey

Kazufumi Manabe
(Visiting Professor, The Institute of Statistical Mathematics)

This paper evaluates the theoretical background of the Japanese National Character Survey. It methodically examines the question items measuring Japanese religious consciousness/religiosity in the 13th and 14th surveys. The theoretical background is explored from the relevant descriptions in various publications about this survey, whereas "structural analysis" and a "item validity approach" are applied to four question items of Japanese religious consciousness/religiosity after checking the frequency distribution tables. The methods used for "structural analysis" are: (1) a correlation matrix, (2) factor analysis, and (3) Cronbach's Alpha. The specific procedures in the "item validity approach" are examinations on (1) the relationships between the socio-demographic items and the religious consciousness/religiosity items, and (2) the relationships between the religious consciousness/religiosity items and the personal-social consciousness and value items.
The results reveal the following:
1. The relevant literature does not explain the theoretical background of these question items.
2. The four religious question items have low internal correlations, consistencies, and reliabilities.
3. The relationships between the socio-demographic items and the religious question items, and the relationships between the religious question items and the personal-social consciousness and value items are, in some cases, inconsistent with the theoretical predictions from the relevant literature.
In the future, the factors influencing these results should be explored. Specific strategies include:
1. Applying mixed-method approaches to explain the results by combining quantitative methods such as factor analysis with qualitative ones such as content analysis of open answers to probe questions.
2. Applying experimental design to systematically investigate the effects of the response styles used in the surveys.

Key words: Japanese National Character Survey, secondary analysis, theoretical background, structure analysis, item validity approach.


Proceedings of the Institute of Statistical Mathematics Vol.69, No.2, 367-388 (2021)

Data Linkage and Machine Learning Approach for Identifying Monetary Policy Effects and Transmission Mechanisms

Katsurako Sonoda
(Department of Statistical Science, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies, SOKENDAI)
Satoshi Yamashita
(The Institute of Statistical Mathematics)

In many empirical analyses of the effects of monetary policy, panel regression analyses are conducted that introduce many dummy variables that cannot be evaluated or interpreted. In such settings, dummy variables can have negative effect to estimation of other variables' true parameters in the regression equation. In this paper, we combined multiple database by data linkage, and then studied the effect of monetary policy, taking advantage of the high prediction accuracy of machine learning. We conducted two analyses. In both analysis, corporate borrowing was used as the dependent variable, and the monetary policy variable was used as the explanatory variable along with other variables. In the first analysis, we estimated the average treatment effect (ATE) of monetary easing or tightening policy using the Double Machine Learning (DML) algorithm in the framework of Rubin's causal effect. In this analysis, the dependent variable is continuous, whereas the monetary p olicy variable is a discrete variable. We consider that the financial variables of banks and firms and macroeconomic environment variables affect the dependent variable and also influence intervention or non-intervention in monetary policy. Our results suggested that monetary policy intervention exerts an effect through firms' balance sheets, but that the size of the effect is small. In the second analysis, we constructed a random forest forecasting model. In this analysis, the dependent variable was discrete and the monetary policy variable was continuous, as monetary policy is expected to affect the decision of whether to increase borrowing, but not the extent of the change in borrowing. Then, we analyzed the sensitivity to monetary policy using the Partial Dependence Plot (PDP), Accumulated Local Effect (ALE), and two-dimensional ALE. The results confirmed that the impact of monetary policy is small, and that monetary policy has a greater impact on the demand for fun ds by firms than on the supply of funds by banks; however, the impact of monetary policy may be due to a change in policy direction rather than the degree of tightening or easing and the extent of the change. We also detected an interaction effect in which smaller banks and banks with lower liquidity holdings are more active in lending to firms under accommodative monetary policy.

Key words: Data linkage, monetary policy effect, average treatment effect, Double Machine Learning (DML), Partial Dependence Plot (PDP), Accumulated Local Effects (ALE).