To consider the jump problem of the Chinese stock market, this paper takes the CSI 300 Index from April 2005 to November 2015 as the research object, uses the rescaled range analysis (R/S analysis) method to examine the fractal characteristics of the Chinese stock market in the past ten years, and deduces the possibility of multiple bubbles in the Chinese stock market. Based on this, combined with the log-periodic power law (LPPL) model, the stock market bubbles are identified in different periods. The results show that China’s stock market has some anomalies in terms of positive bubbles, negative bubbles, and reverse bubbles, as well as the cross occurrence of reverse-negative bubbles. Besides, through a comparison with the major foreign stock markets, it is found that the fluctuation range of the Chinese stock market is much larger than that of the Dow Jones Industrial Average and the FTSE 100 indices in the same period and there are also more types of multibubbles, which is a connotative anomaly that makes the Chinese stock market different from other major stock markets. Furthermore, the bubble phenomenon in the Chinese stock market during the periods of 2005/4–2007/10 and 2015/6–2015/11 is studied, and it is found that there is a jump anomaly in the Chinese stock market. Finally, based on the above empirical analysis and the current state of the stock market, this paper provides some suggestions for improving the mechanism of the Chinese stock market.
The origin of the financial bubble caused by a market jump can be traced back to the 16th Century. At that time, the French government continued to borrow and increase municipal investment, leading to a rapid “boom” in the financial market and the eventual inability of the government to repay what it borrowed, triggering sharp turbulence in the financial market. This encompassed the complete process from bubble to burst due to the early financial market jump anomaly. Of course, the most famous examples of this type of market jump leading to a financial bubble are the tulip mania events in Holland, the French Mississippi bubble events, and the British stock bubble events in the South Sea. The tulip mania events disrupted the Dutch economy completely, which then experienced a rapid financial decline, and the commercial economy transforms from prosperity to decline. The Mississippi bubble caused thousands of banks and tens of thousands of businesses to go bankrupt, and countless people lost their jobs. The South Sea bubble exposed the British government to a century-long crisis of integrity. In addition, the market jump anomaly before and after the US subprime crisis in 2007 dragged the whole world into an economic crisis. It can be seen that financial bubbles generated by market jumps can result in tremendous economic damage. Therefore, it is important to accurately detect and identify market jump anomalies and the underlying financial bubbles. In the context of China, it is important to put forward suggestions and countermeasures that mitigate stock market jumps to promote the healthy development of the Chinese stock market and to maintain stable economic growth.
Prior research on financial market bubbles can be broadly divided into four groups: herd behavior, bubble theory, LPPL analysis, and the market jump anomaly. Among these four groups, the relevant research on herd behavior in the stock market is discussed first. Chen et al. [
It can be found that most of the above studies analyze the formation, development, and bursting of financial market bubbles from a backward perspective. It is difficult to provide forward-looking recommendations for the periodicity and transformation mechanism of market bubbles. The LPPL model, which will now be reviewed, seems to suit this kind of forward-looking problem better. Sornette et al. [
The abovementioned studies are related to the theory of financial bubbles from four aspects: the herding effect, the bubble theory, the LPPL model, and the market jump anomaly. However, for the market jump anomaly, there are relatively few studies on the emergence, development, and bursting of financial bubbles. The Chinese stock market mechanism is not perfect at present, and there is much speculative behavior. This will also lead to the Chinese stock market more easily triggering jump anomalies and financial bubbles than foreign stock markets. Therefore, this paper will measure the bubble anomalies in the Chinese stock market, compare the bubble characteristics of major foreign stock markets, and then study the development of jump anomalies in recent years.
The rest of this paper is organized as follows: Section
The existence of a market bubble is evident to anyone; however, its theoretical background and quantitative description have not been unanimously recognized by academia. Therefore, this section will start with the definition of a market bubble and combine the fractal theory and the LPPL model from this field to analyze the feasibility of market bubble detection and identification.
A common and simple definition of a market bubble is that a financial asset or a series of financial assets experience a sharp rise in market prices relative to their real values or there is a continuous plunge in financial assets, resulting in market values falling below their real values [ Positive bubble: the price has a sharply rising trend, with the price rising above its actual value, and the rising trend gradually increases. See Figure Negative bubble: the price has a sharp downward trend, with the price falling below its actual value, but the downward trend gradually weakens. See Figure Reverse bubble: the price has a sharp downward trend, with the price falling below its actual value, and the downward trend gradually increases. See Figure Reverse negative bubble: the price has a rising trend, with the price rising above its actual value, but the rising trend gradually weakens. See Figure
Positive bubble morphology.
Negative bubble morphology.
Reverse bubble morphology.
Reverse-negative bubble morphology.
Figures
The development of bubble theory includes rational bubbles and the irrational bubbles along with the linear bubble and the nonlinear bubble. Consequently, many bubble detection methods and measurement theories have been derived. In recent years, financial physics classification theory and the LPPL model have been applied successfully to domestic and foreign financial markets; therefore, the present study is based on these two theories. In this paper, the fractal theory is mainly applied to measure the fractal characteristics of financial markets and then to judge whether the market has a positive feedback effect and whether the market has the resulting bubble phenomenon. The relevant theoretical analysis is as follows.
The fractal dimension is an important quantitative representation or basic parameter for studying market bubbles using fractal theory. It is not only the characteristic quantity describing fractal time series, but it can also be used to measure the degree of unevenness of time series, which are generally expressed by numbers with decimal points. The fractal dimension of a straight line is 1, the fractal dimension of a plane is 2, and the fractal dimension of a random walk between a straight line and plane is 1.5. In the calculation of the fractal dimension of a financial market, the most commonly used method is
First, transform the financial transaction data according to equation (
Second, take
Furthermore, the residual sequence is divided into equal-length intervals of
Take the logarithm on both sides of equation (
Fractal theory can effectively find the similarity between the whole and the part, the chaos and the rule, and the transition between order and chaos and apply these concepts to financial markets to deepen our understanding of them. When the fractal dimension is from 1 to 1.5, the smoothness of the rate of return series is between a straight line and a random walk, the fractal structure is relatively stable, and the historical increments promote future incremental growth. This makes it is easy for a market bubble to form. Of course, fractal theory can simply detect the existence and relative strength of a bubble, but it cannot judge the duration of the bubble, the magnitude of the bubble, or the reversal time of the bubble. Therefore, further study of the existence of bubbles by using the LPPL model will be an effective supplement.
As mentioned above, the main reason for stock market bubbles is the mutual imitation of traders, which triggers a positive feedback effect in the market, and this in turn leads to rapid price increases. Some researchers have conducted theoretical studies and constructed the descriptive models of the phenomenon. Among them, a seminal study is the study of Johansen and Sornette [
According to Greenwood and Nagel [
The LPPL model compares the market collapse with a critical point and uses the power law to fit the price or its logarithm. Because traders imitate each other and form collective effects through positive feedback, the price is similar to logarithmic periodic vibration; therefore, a final market collapse can be explained by market dynamics, which are also the theoretical basis of the LPPL model.
Based on the history of the development of the Chinese stock market, we can subjectively find that since 2006, the stock market has started to form bubbles and exhibit certain jumps. In 2007, the CSI 300 index broke through 5800 points, and then it fell rapidly in 2008, reaching a minimum of 1627.76 points. The extent of the decrease was over 72%. Besides, since the end of 2014, the stock market has entered another round of continuously increasing and jump. The CSI 300 index broke through 4000 points on March 30, 2015, a new 7-year high. Then, it broke through 5000 points on May 25, 2015, until it reached 5353.75 points. The continuous jump in the stock index has aroused the
To study the bubbles and jumps in the Chinese stock market, the present study selected the transactional data of the CSI 300 index from April 8, 2005, to November 5, 2015, as the research sample. The CSI 300 index is compiled by grading technology based on liquidity and market value and is comprised of 300 A-shares selected from the Shanghai and Shenzhen stock markets through a certain screening process. The CSI 300 index tends to reflect the trends of the Shanghai and Shenzhen markets as a whole, and the return of mainstream investment. The trading points of the CSI 300 index were collected as sequential data for the present study, with 2570 data collected in total. The specific trend is shown in Figure
Trend chart of the CSI 300 index.
As seen from Figure
Trend chart of the CSI 300 index yield rate jump.
The basic statistical characteristics of the rate of return of the CSI index.
Sample | Mean value | Mid value | Standard deviation | Skewness | Kurtosis | Jarque–Bera | Number |
---|---|---|---|---|---|---|---|
CSI 300 index | 0.0000674 | 0.000128 | 0.00245 | −0.428 | 6.331 | 1265.884 | 2569 |
Through the analysis of Table
To detect whether there is a bubble in the sample interval, we used
The
CSI 300 index | |
---|---|
0.7284 | |
0.6836 | |
0.6714 |
The results of the
The results of the
The results of the
From Table
Based on the above analysis, we can see that, in the above modeling interval, there are jump anomalies and the necessary conditions for bubbles in the Chinese stock market. Furthermore, the bubbles have the potential to greatly harm investors or the whole economy and may lead to the market’s collapse and an economic crisis. Therefore, identifying the types of bubble and predicting the collapse of bubbles (mechanism transformation) is of great significance.
The phenomenon of jump anomalies in the Chinese stock market is mainly reflected in the corresponding market bubble. The following outlines the use of the LPPL model to identify various bubbles in the Chinese stock market and to further analyze the relative bubble size and the mechanism transformation time. Besides, the two largest bubbles in the period are compared, and the causes are analyzed.
The stage division in Table
Jump transformation time of CSI 300 index returns.
Time quantum | Transformation time | Time quantum | Transformation time |
---|---|---|---|
2005/4–2007/10 | 2008/1/14 | 2012/1–2012/4 | 2012/5/7 |
2007/11–2008/10 | 2008/11/5 | 2012/5–2012/11 | 2012/12/3 |
2008/11–2009/7 | 2009/8/3 | 2012/12–2013/6 | 2013/6/27 |
2009/8–2009/11 | 2009/12/7 | 2013/7–2014/5 | 2014/6/6 |
2009/12–2010/6 | 2010/7/5 | 2014/6–2015/5 | 2015/6/11 |
2010/7–2010/10 | 2010/11/8 | 2015/6–2015/11 | — |
2010/11–2011/12 | 2012/1/5 | — | — |
Unit root test of price return of metal futures.
Up jump | Down jump | Small jump of transverse disk | Transition stage |
---|---|---|---|
2005/4–2007/10 | 2007/11–2008/10 | 2009/8–2009/11 | 2012/1–2012/4 |
2008/11–2009/7 | 2009/12–2010/6 | — | 2012/5–2012/11 |
2010/7–2010/10 | 2010/11–2011/12 | — | 2013/7–2014/5 |
2014/6–2015/5 | 2012/12–2013/6 | — | — |
— | 2015/6–2015/11 | — | — |
In Table
LPPL model fitting of the rate of return of CSI 300 index.
Time quantum | Bubble morphology | |||||||
---|---|---|---|---|---|---|---|---|
2005/4–2007/10 | 0.0293 | 1.8975 | −197.806 | 7.7938 | −0.0530 | 0.7707 | 2008/1/8 | Bubble |
2007/11–2008/10 | 0.5807 | −13.313 | −39.9702 | 7.1852 | −0.0599 | −0.0048 | 2008/11/14 | Reverse bubble |
2008/11–2009/7 | 0.7520 | −17.968 | 6.7555 | 8.2478 | −0.0156 | −0.0014 | 2009/8/3 | Reverse-negative bubble |
2009/8–2009/11 | 0.4599 | −35.915 | 35.430 | 18.792 | −23.903 | −0.3169 | 2009/12/23 | — |
2009/12–2010/6 | 0.7557 | 9.6010 | −286.34 | 8.3643 | −10.076 | −1.3509 | 2010/7/11 | Reverse bubble |
2010/7–2010/10 | 0.3495 | −4.9952 | 11.372 | 8.4486 | −0.1240 | −0.0124 | 2010/11/18 | — |
2010/11–2011/12 | 0.3331 | 12.362 | −52.269 | 7.6212 | −0.0750 | 0.0068 | 2012/1/6 | Reverse bubble |
2012/12–2013/6 | 0.3769 | 4.5453 | −19.081 | 8.0244 | −0.8004 | −0.2039 | 2013/7/2 | — |
2014/6–2015/5 | 0.5504 | 11.520 | −20.875 | 9.2901 | −0.0740 | 0.0039 | 2015/6/14 | Bubble |
2015/6–2015/11 | 0.0563 | −0.4777 | 339.04 | 13.263 | −24.062 | 5.3505 | 2015/12/08 | Negative bubble |
In Table
Fitting results from 2005/4 to 2007/10.
Fitting results from 2007/10 to 2008/10.
Fitting results from 2008/11 to 2009/7.
Fitting results from 2009/8 to 2009/11.
Fitting results from 2009/12 to 2010/6.
Fitting results from 2010/7 to 2010/10.
Fitting results from 2010/11 to 2011/12.
Fitting results from 2012/12 to 2013/6.
Fitting results from 2014/6 to 2015/5.
Fitting results from 2015/6 to 2015/11.
Fitting results from 2005/4 to 2015/11.
By comparing
From Figures
Furthermore, from Figure
This study confirms that from April 2005 to October 2007, thanks to the improvement of macroeconomic policies, the Chinese stock market experienced a continuous rise/jump, which eventually led to the jump anomaly in the stock market. Before this round of gains, the China Securities Regulatory Commission issued a “notice on issues related to the pilot reform of nontradable shares of listed companies,” announcing the launch of the pilot reform of nontradable shares, which eliminated the differences between tradable shares and nontradable shares. To a certain extent, this solved the problem of balancing the interests among the relevant shareholders in the A-share market and ushered in a brand new period in the development of the Chinese stock market. Following this, the stock market flourished, the rate of return increased unceasingly, and market speculation and irrational investment increased massively. The market had entered the phase of the jump anomaly. Finally, the bubble burst in January 2008, and the CSI 300 index fell sharply, from 5699.15 points to 1627.76 points. After approximately 7 years of jumps up and down, in June 2014–May 2015, there was a new upward trend. At this stage, both the uptrend and the height were at least as good as those of the previous phase. Figures
Taking the CSI 300 index as a research object, we have used the
These jump anomalies in the stock market are not only related to the rise and fall of the stock market, but they can also have a large impact on the national economy. Our findings suggest that the relevant departments in China should introduce a mechanism for stock market bubble detection, identification, prevention, and treatment and then effectively measure and respond to stock market bubbles and jump anomalies. It is noted that there are also some limitations to this study. The researches of this paper were primarily focused on the fractal and periodic power law measures of stock market bubbles, and there is no analysis of the causes of stock market bubbles. Furthermore, the methods on how to deal with an uncontrollable stock market bubble and the market over-jump anomaly have not been discussed in this paper. Therefore, further studies on such issues could be important and interesting [
The data used to support the findings of this empirical study can be downloaded at
The authors declare no conflicts of interest.
This work was supported by the Social Science Youth Foundation of the Ministry of Education of China under Grant 18YJC790118 and Natural Science Foundation of China (No. 71764033).