Co-Citation Analysis and Burst Detection on Financial Bubbles with Scientometrics Approach

It is found that financial crises generally happen accompanied by the collapse of financial bubbles. Therefore, many scholars have carried out researches on financial bubbles. In this paper, we analyse the current status and explore the development of financial bubbles with scientometric technique. By downloading and analysing 1048 articles from Web of Science, the main findings of this paper are: 1) Three hot topics in the financial bubble research are ‘Ledoit-Sornette financial bubble model’, ‘European Union emission trading scheme’ and ‘agent-based model’; 2) the current research status of financial bubble is clearly demonstrated by the most productive subject categories, countries, institutions, journals, authors, and cited articles; 3) the investigations that related to ‘Chinese stock market’ contribute significantly in the financial bubble research; and 4) the burst detection analysis shows that the new trends in recent years are ‘asset price bubble’, ‘herd behaviour’, ‘crashes’, and ‘econophysics’. Therefore, this paper provides the knowledge domain, the overall intellectual structure, and the emerging trends of the financial bubble research by analysing the status quo, the co-citations, and the burst detection, which presents more accurate and comprehensive insights into research topics and research development trends over time from various perspectives. ARTICLE HISTORY Received 26 September 2018 Accepted 11 March 2019


Introduction
Financial bubbles are common phenomena in financial and economic development. The formation and collapse of financial bubbles not only cause great losses in financial markets but also lead to great harm to the economy of a country. Moreover, the decrease in citizens' real income and the bankrupting of enterprises after the bubble burst both results in sluggish consumer demand, deflation, and even economic recession. There are many typical cases in history, such as the bubble crisis of the South Sea in 1720, the case of a tulip in 1637 and the subprime mortgage crisis in 2007. (Pan, Zhao, Li, et al., 2017). Therefore, the arrival of CiteSpace has inspired scholars in various fields, telling them that there are still some new fields to be explored. However, there exists a lack of researches on financial bubbles based on scientometric analysis.
Due to the above and the growing number of publications which investigate financial bubbles, it is significant to learn about the current status and the developmental trends in financial bubble researches. The contributions that this paper made are: 1) the status quo, the co-citation analyses, and the burst detection are quantitatively analysed to provide scholars with a more comprehensive insight of financial bubble research; and 2) the overall intellectual structure and the emerging trends of financial bubble research are presented visually, which is helpful for scholars, especially for beginners to learn more about this research field.
To achieve the above aims, the remainder of this paper is organised as follows: Section 2 introduces the data collection and research method, in which the source of data, the corresponding operational process, and relevant techniques are discussed. The Publication number, citation, and hot topic analyses are demonstrated in Section 3. Section 4 is about the current research status of financial bubble research based on the statistics of categories, sources, authors, countries, and institutions in the financial bubble field. Section 5 demonstrates the burst detection in financial bubble research, informing the potential research directions. Finally, Section 6 is the summary, which includes general conclusions and the expectations of this paper.

Data collection and research method
In order to illustrate how the data are analysed by utilising CiteSpace, the process is introduced on the aspects of data collection and research method. We provide an architecture diagram to briefly summarise the whole analytic process. The explanation of some significant terms and indexes with the corresponding algorithms are shown to present how the techniques work on further analyses in the following sections.

Data collection and architecture diagram
In this study, Web of Science (WoS) is our main data source due to the reason that it is a large platform that enables individuals to know the detailed information of the articles published in approximately 12,000 leading journals worldwide. Besides, the Science Citation Index Expanded (SCI-EXPANDED), the Social Science Citation Index (SSCI) and the Arts & Humanities Citation Index (AHCI) databases are included in WoS (Leeuwen, 2006), making the analytic results more accurate and comprehensive. It should be explained that to eliminate the 'noise' that could impact the results' accuracy, the references published in some databases such as Conference Proceedings Citation Index-Science, Emerging Sources Citation Index and Book Citation Index-Science are not in the scope of consideration in this study. Thus, when searching the research topic 'financial bubble', a total of 1048 articles can be shown. The relevant data were downloaded from WoS on 26 October 2017. In order to make the whole procedure more understandable, an architecture diagram is given in Figure A1 to show the details of the data analysis.

Data analysis and research method
Some important terms and indexes in Figure A1 are explained to clarify how the techniques work, which further supports the reasonability of the analytic results.
Time slice: The method to divide a period of time into a series of smaller windows. Threshold: A selection of criteria which selects items in the modelling and visualizing of the process. Top N: The top N frequently cited articles are selected Top N%: The articles are selected primarily on the basis of citations, then the top N% of them are finally chosen. C, CC, CCV: Citation, co-citation, and cosine coefficient. CC(i,j) is the co-citation number of reference i and reference j. C(i) and C(j) are their citation number, respectively. Suppose that in a certain time period, the co-citation number of reference i and reference j is 2. Reference i is cited four times, while reference j is cited three times, then we have CCV ¼ 2=sqrtð4 Â 3Þ%0:577 . Density: The ratio of the actual relations to the utmost relations in a network. Silhouette: The value that measures the quality of a clustering configuration with the range between -1 and 1. A higher silhouette value indicates a more perfect solution. Basically, the clustering results are efficient and reliable when their silhouette values are bigger than 0.7, and the results can be reasonable when their values are bigger than 0.5.
As mentioned before, some information such as the keywords, journals, and reference that appear or co-cited with high frequency can be found by CiteSpace by choosing different node types. An important index which identifies the above nodes is betweenness centrality. The betweenness centrality is defined in Eq. (1).
In Eq. (1)., d jk indicates the number of the shortest paths between node j and node k . Also, d ik ðiÞ is the number of abovementioned paths which pass through the node i . For instance, an article with high betweenness centrality is relatively more significant in a co-citing network (Li, Porter, & Wang, 2017). In this paper, different articles and the relevant clusters with significant influence are illustrated based on the value of betweenness centrality. Furthermore, as analysed in the following sections, the timeline of the most cited references, the articles and the keywords that received strong citation burst are also determined according to this crucial index.
3. Publication number, citation, and hot topic analyses

Publication number and citation analyses
The financial bubble stems from Tulipmania in Holland in 1637 (Garber, 1989). However, the tulip bulbs were unusually appealing at that time, triggering a scramble for them. After that, the price of tulip soared rapidly. After the bubble bursts in 1637, the tulip was worth only 1% of the price in a bubble, leaving all major Dutch cities in chaos. Same cases never come to an end, the South Sea Company suffers a financial bubble in 1720 (Carswell & Goodison, 1960) and the world falls into the great depression from 1920 to 1933 (Lucore, 1991). In the late twentieth century, the global economy burst out another financial bubble that consisted of a real estate bubble in Japan (Kim & Suh, 1993). The advent of financial bubbles usually brings serious crises to countries and regions. As a kind of systematic financial risk, it encourages scholars to research on avoiding and dealing with financial bubbles from different industry risks and different levels of regulatory measures.
In order to present the current status and the emerging trends in financial bubble research, the paper sorts out the publications and citations primarily in this field. It can be learned from Figure A1 that the topic of financial bubbles has obtained growing attention. The quantity of publications about financial bubbles is increasing every year. Specifically, the number of the 1048 articles' citations per year from 1994 to 2017 is shown in Figure A2. According to the statistics in Figure A2, the citations of financial bubbles are also increasing every year. In other respects, the 1048 articles are cited 12,499 times apart from the self-citations by October 26 2017, and 13.27 times for an average article. It should be noted that there are two months left in 2017, hence the articles published in these two months cannot be obtained due to retrieval delay. However, the number of articles published in 2017 is predicted to increase because there are about 100 publications each year from 2011 to 2016 in the field of financial bubbles. On the other hand, the growth of publications has slowed down in the past five years because the related research methods are still limited, and many fields have been investigated repeatedly. However, the bursts still exist, which is the new direction of financial bubble researches. More information is given below.

Hot topic analysis
This subsection illustrates the research focus and hot topic of financial bubbles through cluster analysis. The position of clusters and the association among clusters in co-citation networks displays the intellectual structure in science mapping. It is easy to take a clear view of the whole picture in financial bubble researches. Figure  A3 shows the cluster network in the financial bubble field. The clusters are labelled by index terms from their own citers. Meanwhile, the fields that are coloured differently indicate the time when co-citation links in those fields appear for the first time, and the fields in yellow are earlier than the ones in red. Moreover, the summary of the largest 10 clusters in financial researches is shown in Table A1.
The size in Table A1 demonstrates the number of publications in the cluster. For more details, please see Figure A4. For instance, the cluster (#0) has 66 members, which is one of the largest clusters in the financial bubble field. The second cluster (#1) and the third cluster both have 65 members. On the other hand, Silhouette is an index to measure the homogeneity of a cluster, the greater the value of this index the better the homogeneity. LLR (log-likelihood ratio) is a kind of algorithm according to the probability density function to determine the maximum likelihood and find the most likely words. The index of Mean (Year) in Table A1 represents the average published articles per year of the nominated cluster. It can be learned that the cluster 0, cluster 1, cluster 4, and cluster 8 are the main clusters in the research field of financial bubbles, which are 'Ledoit-Sornette financial bubble model', 'European Union emission trading scheme', 'Asset market', and 'Macro risk', respectively. Obviously, two of the three largest clusters investigate the significant models in the financial research area, namely the Ledoit-Sornette model which is also the Johansen-Ledoit-Sornette (JLS) model and the agent-based model. By applying these two models, some scholars have made great contributions in terms of theoretical improvement and empirical investigation.
Specifically, the JLS model is proved to own the predictive power to diagnose the times of major marker rebounds (Yan, Woodard, & Sornette, 2012). Moreover, Sornette, Woodard, Yan, and Zhou (2013) reviewed the general problems of the JLS model and summarised the status quo of it and existing best practice. There are also some improvement methods proposed to further optimise the application of the JLS model. For instance, Filimonov and Sornette (2013) proposed a simple transformation of the calculating process in this model to decrease the complexity and improved efficiency. In consideration of the agent-based model (ABM), it is also a useful tool for researchers to observe, investigate, and simulate the diversity, dynamics, and interdependence in financial markets. Samanidou, Zschischang, Stauffer, and Lux (2007) reviewed some microscopic (agent-based) models utilised in financial markets. Based on the ABM, some phenomena have been studied in financial markets, e.g., Alfi, Cristelli, Pietronero, and Zaccaria (2009) proposed a minimal agent-based model to learn the nature and self-organisation of the stylised facts in capital markets. Also, Lengnick and Wohltmann (2013) integrated the theory of ABM and a New Keynesian macroeconomic model, then gave some suggestions based on the corresponding simulation.
In general, the results of the clusters are satisfactory according to the value of silhouette in Table A1 and the classification of colours in Figure A3. It is desirable to define the specialties in science mapping in terms of co-citation clusters. Moreover, the topic of 'Ledoit-Sornette financial bubble model' has more potential for further researches due to the high cluster.

Current research status of the financial bubble
In order to clarify the current state of financial bubble researches, this section sorts out the significant subject categories and productive sources, authors, countries, and institutions in financial bubble research to give a detailed illustration. Table A2 illustrates the top 10 subject categories in financial bubble research. It can be found that 'Business Economics' is the most popular subject category with 681 publications which account for 64.734% of the total publications. The second is 'Physics' and the third is 'Mathematics', which indicates that the researches on financial bubbles mainly utilise physical and mathematical methods. The following categories are 'Government Law', 'Mathematical Methods in Social Sciences', 'Environmental Sciences Ecology', 'Geography', 'Social Sciences other topics', 'Urban Studies', and 'Computer Science'. Table A3 and Figure A5 show that Physica A: Statistical Mechanics & Its Applications is the most productive source with 65 publications which account for 6.179% of the total publications. According to the categories published from Physica A: Statistical Mechanics & Its Applications, it can be found that this journal mainly introduces statistical mechanics (to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents) and widespread applications of the techniques of statistical mechanics, such as physical systems, economic and sociological systems. According to Table A2, there is no doubt that Physica A: Statistical Mechanics & Its Applications is the most productive source in the financial bubble field.
There are hundreds of scholars worldwide to carry out researches on financial bubbles. Table A4 illustrates the top 10 most productive authors in this field. Sornette, who contributes theoretical models, empirical tests of the detection and operational implementation of financial bubble forecasts, is the most productive author. The LPPLS (Log-periodic Power Law Singularity) model was first proposed by Sornette et al. in 1995 as a theoretical formulation of the acceleration moment release to predict earthquakes . Then, the LPPLS model was applied to analyse financial bubbles and their burst by Sornette (Sornette et al., 1996). Based on Table A1, it is obvious that Sornette is leading a new way to carry out researches on financial bubbles today.
The development of the researches on financial bubbles differs from country to country. Table A5 shows the top 10 most productive countries in this research. The U.S.A. is the most productive country in financial bubble research followed by England, Germany, People R China, France, Italy, Japan, Spain, Switzerland, and Canada.
Since the establishment of the financial markets in western countries is early historically, the economic development in those countries is more normative and more mature than in any other countries. Table A6 shows that the University of Geneva from Switzerland contributes the most publications in financial bubble research with 24 publications. The second is the Swiss Federal Institute of Technology Zurich from Switzerland and the third is the University of California-Los Angeles from the U.S.A. Among the top 10 institutions in Table A6, five of them are from the U.S.A. Switzerland and England both have two and one is from Germany. However, China, France, Italy, Japan, Spain, and Canada are the most productive countries in terms of financial bubble researches, but there is no productive research institution in these countries. Figure A6 shows the timeline of the top 20 cited articles in each year. It provides an intuitive and accurate way to understand the evolution path of each sub-field. It can be learned that there are many significant achievements from 1997 to 2016 in financial bubble research. The researches mainly investigate the 'agent-based model' and the 'Log-periodic precursor' from 1997 to 2000. Moreover, scholars focus more on 'Asset bubble', 'Chinese stock market', and 'Modern rheology' from 2000 to 2010. The 'Bubble indicator' and 'European Union emission trading scheme' have become the current research subbjects from 2010 to 2016. Additionally, there are many types of research about 'bubble indicator' and 'European Union emission trading scheme' based on the researches of the 'Chinese stock market'. Compared with the research directive of financial bubbles, more articles are published and cited in the 'Asset bubble' Class.
Today, many types of research on financial bubbles are inspired by China's stock market. Both China and Chinese scholars are ranked in the top 10 in Tables A4 and A5, but the most productive institutions are from the U.S.A., Switzerland, England and Germany. This implies that more should be done to develop financial bubble institutions in China. Setting up the special departments to carry out researches on financial bubbles is of great necessity.

Burst detection in financial bubble research
Burst detection will make it possible to find the articles that receive particular attention from the related scientific communities in a certain period of time. It should be noted that a research cluster containing a certain quantity of articles with citation burst can be considered as a new research field. In order to reveal the potential research directions, this paper selects the references with citation bursts and keywords with bursts to explain the focus of financial bubble researches in a different time. Table A7 illustrates the top 20 references with strongest citation bursts. In the last columns, the length of the line represents the period from 1945 to 2017, in which the red line means the time period of citation bursts. It is clear that more bursts arise in the second half of the whole time period. The first one ranked in Table A7 is  with a burst strength of 6.8111, followed by  with a burst strength of 5.3726. Table A8 lists the top 10 keywords with bursts, which are the fast-growing topics in financial bubble research. Different keywords with bursts represent the corresponding characteristics in each time period. 'Herd behaviour' is first proposed in stock investment. Banerjee (1992) pointed out that the herd behaviour is a 'behaviour that people do what other people are doing even though their own private information suggests that the behaviour should not be taken', which is to say an individual takes the same action as any other person takes despite private information. Shiller (1995) defines herding as a way of thinking and behaving such that people in an interacting community tend to behave similarly.
Some financial crisis bursts from 1992 to 2007, such as the financial crisis in Mexico from 1994 to 1995, the financial crisis in Southeast of Asia in 1997 and the financial crisis triggered by the subprime mortgage crisis in 2007. The researches on 'herd behaviour' imply that the phenomenon is more serious than at any other time, leading to the financial bubble bursts. Moreover, 'Econophysics' was first proposed by Stanley from Boston University in 1995, which has been developed as an emerging subject. 'Econophysic' bursts arose almost at the same time period with 'Herd behaviour', 'Crashes', and 'Fluctuation'. It is popular to use statistical physics, complex systems theory, applied mathematics, and other methods to observe the formation and collapse of the bubble quantitatively in a financial crisis. The burst detection of keywords is to find the high-frequency words or phrases in the literature at different time intervals. In 2013, some big events took place such as the U.S. withdrawing from quantitative easing and the European Central Bank cutting interest rates twice during the year to promote the economy. Furthermore, Bitcoin prices have gone from $20 at the beginning of the year to $1,200. These international events have caused the discussion on 'asset price bubbles'. Hence, the keyword 'asset price bubbles' bursts from 2013 to 2015, which means it has been mentioned more times than any other terminologies in a short time period.
Generally, 'Bubbles, fads, and stock price volatility tests: a partial evaluation' by West in 1998 is an important article which indicates the long-term trend with high bursts. Today, 'asset price bubble' is popular in financial bubble researches. In both industrialised and developing countries, the sharp fluctuations in asset prices have become a prominent phenomenon in the macroeconomy. Therefore, it is essential to find an efficient and appropriate level of supervision measure to investigate the price change and to avoid the financial bubbles.

Conclusions
This paper provides a scientometric review of financial bubble studies by CiteSpace based on 1048 articles from Web of Science. According to the analyses above, some conclusions are derived as follows: 1) 'Business Economics', 'Physics', and According to the visualization analysis and review of the articles about financial bubbles, it is easy for readers to obtain a better understanding of the trends in financial bubble research. From different perspectives of bibliometric analysis, we provide an overview about the current status and the emerging trends of financial bubble research, which helps researchers who are interested in knowing the general picture of this knowledge domain understand the dynamics of hot spots in the last few decades. According to the current research status in different countries, some of them with little achievements in financial bubble research should focus more attention on it. On the other hand, this paper offers a picture of the directions in the financial bubble researches, which helps the researches step into a mature stage. Financial bubble risk as a kind of systematic financial risk is a result of a dynamic game between financial institutions and supervision departments. How to balance the relationship between supervision and innovation is still a problem.
In China, the report of the 19th National Congress specifically stated that it is necessary to improve the financial supervision system and maintain the bottom line of systemic financial risks. In the reconstruction of the financial regulatory framework reform, although the Financial Stability Development Committee was established in 2017, and new regulations such as assets were introduced, many institutional challenges were still faced. How to create an effective financial supervision system that encourages financial innovation and balances stability, efficiency and fairness has become a top priority for the Chinese government.        Table A7. Top 20 references with the strongest citation bursts.