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We choose 100 stocks from China's markets and use their daily returns from January 3, 2013 to August 31, 2020 to investigate the risk situation in China's stock markets by exploring their correlations in the sample period. We build complexes and carry out topological data analysis on them. The persistence landscapes and their LP-norms show that there are three clear turbulent periods since 2013. The dates are then detected when the stocks are strongly correlated. As is well known, the financial risks easily break out and spread in such situations, so we call the dates critical dates for risks. We can also take them as the early warning signals for potential risks. We then construct planar maximal filtered graphs on the critical dates to help discover the systematically important companies. We find that they changed obviously in three different turbulent periods. It reminds us to analyze the risks' characteristics of the risks and implement risk prevention. The method combing topological data analysis and complex networks is shown to be effective in detecting critical information from markets, and hence is worth popularizing. [ABSTRACT FROM AUTHOR]

This paper explores the links between the USD/RMB and the Shanghai Stock Index using the ARCH model. The key findings are: the USD/RMB exchange rate and the Shanghai Stock Index are in equilibrium in the long-run; USD/RMB exchange rate is the leading indicator of Shanghai stock index; spot exchange rate is positive to Shanghai Stock Index; spot exchange rate is negative to Shanghai Stock Index in 1 lag; exchange rate movements are significant to stock market volatility when the fixed exchange rate regime is changed into a managed floating exchange rate regime. [ABSTRACT FROM AUTHOR]

Using homogenous partition of coarse graining process, the time series of Hang Seng Index (HSI) in Hong Kong stock market is transformed into discrete symbolic sequences S={S1S2S3⋯}, Si∊(R, r, d, D). Weighted networks of stock market are constructed by vertices that are 16 2-symbol strings (i.e. 16 patterns of HSI variations), and encode stock market relevant information about interconnections and interactions between fluctuation patterns of HSI in networks topology. By means of the measurements of betweenness centrality (BC) in networks, we have at least obtained 3 highest betweenness centrality uniform vertices in 2 order of magnitude of time subinterval scale, i.e. 18.7% vertices undertake 71.9% betweenness centrality of networks, showing statistical stability. These properties cannot be found in random networks; here vertices almost have identical betweenness centrality. By comparison to random networks, we conclude that Hong Kong stock market, rather than a random system, is statistically stable. [ABSTRACT FROM AUTHOR]

We analyze financial time series based on topological data analysis to obtain the critical information around 2008 global financial crisis and 2010 European debt crisis. We build an early warning system to detect the critical dates on the financial time series. By constructing complexes on the point clouds data with sliding windows, we explore their topological changes from window to window. The persistence barcodes, diagrams and landscapes are obtained from the complexes of several US's stock indices. We detect the early warning signal of the 2008 crisis in the first half of 2007. The changes of complexes are also shown in detail. And then we choose several European countries' typical indices to do a similar work. The topological structures of the complexes change sharply in 2008 and 2010. It shows us clearly that 2008 and 2010 financial crises affected European stock markets greatly. To study the condition of China's stock markets during the crises, we choose two major stock indices to construct complexes and analyze their changes. The early warning signal is also detected in the early 2007, and China's stock markets experienced quite a long period of intense turbulence around 2008. However, it was not so serious as US's and European markets. Furthermore, we also see that European debt crisis did not obviously affect China's stock markets. • An early warning system based on topological data analysis is built to detect the critical dates on the financial time series. • The persistence barcodes, diagrams and landscapes are obtained on the complexes of some chosen indices from US, Europe and China. • The early warning signals are detected with the help of the early warning system. • Point clouds data are analyzed in detail around 2008 global financial crisis and 2010 European debt crisis. [ABSTRACT FROM AUTHOR]