Precision measurement of the return distribution property of the Chinese stock market index

Systematical and precise analysis on the 1-min datasets over the 17-year period 2005-2021 for both the Shanghai Stock Exchange and the Shenzhen Stock Exchange composite index is conducted in this paper. Here we precisely measure the property of return distributions of composite indices over time scale $\Delta t$ ranging from 1 min up to almost 4,000 min, to reveal the difference between the Chinese stock market and the mature stock market in developed countries. The return distributions of composite indices for both exchanges show similar behavior. Main findings in this paper are as follows. (1) The central part of return distribution is well described by symmetrical L$\acute{e}$vy $\alpha$-stable process with stability parameter comparable with the value of about 1.4 extracted in the U.S. stock market. (2) Distinctively, the stability parameter shows a potential change when $\Delta t$ increases, and thus a crossover region located at 15 $< \Delta t <$ 60 min is observed, which is different from the finding in the U.S. stock market where a single value of about 1.4 holds over 1 $\le \Delta t \le$ 1,000 min. (3) Return distributions can be also well described by the student's distribution within wider return range than the L$\acute{e}$vy $\alpha$-stable distribution. (4) The tail distributions of returns at small $\Delta t$ decay as asymptotic power law with exponents being about 3, which is a value widely existed in mature stock markets. However, it decays exponentially for $\Delta t \ge$ 240 min, which is not observed in mature markets. (5) The return distributions slowly converge to Gaussian along with $\Delta t$ increasing, which is also different from the finding of a critical $\Delta t = 4$ days in the U.S. stock market

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page

From Big Data to Econophysics and Its Use to Explain Complex Phenomena

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Three Risky Decades: A Time for Econophysics?

Our Special Issue we publish at a turning point, which we have not dealt with since World War II. The interconnected long-term global shocks such as the coronavirus pandemic, the war in Ukraine, and catastrophic climate change have imposed significant humanitary, socio-economic, political, and environmental restrictions on the globalization process and all aspects of economic and social life including the existence of individual people. The planet is trapped—the current situation seems to be the prelude to an apocalypse whose long-term effects we will have for decades. Therefore, it urgently requires a concept of the planet's survival to be built—only on this basis can the conditions for its development be created. The Special Issue gives evidence of the state of econophysics before the current situation. Therefore, it can provide excellent econophysics or an inter-and cross-disciplinary starting point of a rational approach to a new era

Complex systems approach to natural language

The review summarizes the main methodological concepts used in studying natural language from the perspective of complexity science and documents their applicability in identifying both universal and system-specific features of language in its written representation. Three main complexity-related research trends in quantitative linguistics are covered. The first part addresses the issue of word frequencies in texts and demonstrates that taking punctuation into consideration restores scaling whose violation in the Zipf's law is often observed for the most frequent words. The second part introduces methods inspired by time series analysis, used in studying various kinds of correlations in written texts. The related time series are generated on the basis of text partition into sentences or into phrases between consecutive punctuation marks. It turns out that these series develop features often found in signals generated by complex systems, like long-range correlations or (multi)fractal structures. Moreover, it appears that the distances between punctuation marks comply with the discrete variant of the Weibull distribution. In the third part, the application of the network formalism to natural language is reviewed, particularly in the context of the so-called word-adjacency networks. Parameters characterizing topology of such networks can be used for classification of texts, for example, from a stylometric perspective. Network approach can also be applied to represent the organization of word associations. Structure of word-association networks turns out to be significantly different from that observed in random networks, revealing genuine properties of language. Finally, punctuation seems to have a significant impact not only on the language's information-carrying ability but also on its key statistical properties, hence it is recommended to consider punctuation marks on a par with words.Comment: 113 pages, 49 figure

Complexity in Economic and Social Systems

There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure