رفتار دسته بندی زمانی از دنباله نوسانات شدید در بازارهای بورس چینی

Sharp fluctuations (in particular, extreme fluctuations) of asset prices have a great impact on financial markets and risk management. Therefore, investigating the time dynamics of sharp fluctuation is a challenge in the financial fields. Using two different representations of the sharp fluctuations (inter-event times and series of counts), the time clustering behavior in the sharp fluctuation sequences of stock markets in China is studied with several statistical tools, including coefficient of variation, Allan Factor, Fano Factor as well as R/S (rescaled range) analysis. All of the empirical results indicate that the time dynamics of the sharp fluctuation sequences can be considered as a fractal process with a high degree of time-clusterization of the events. It can help us to get a better understanding of the nature and dynamics of sharp fluctuation of stock price in stock markets.

Sharp fluctuations (in particular, extreme fluctuations) of asset prices have a great impact on financial markets and risk management. Therefore, investigating the time dynamics of sharp fluctuation is a challenge in the financial fields. Many scholars showed their interests on this issue and found some meaningful conclusions. Chen et al. [1] analyzed the daily Hang Seng index in the Hong Kong stock market. They predicted the future price movements using two kinds of sign sequences as given conditions. One is the parameter of multifractal spectrum Δf based on the indexes recorded in every minute, and the other is the variation of the close index Δi. Results show that correlation between large fluctuations of the close price and the condition in these two methods is strong and some sign sequences of the parameter Δf can be used to predict the probability of the near future price movements. Muchnik et al. [2] studied the long term memory in extreme returns of financial time series and revealed that the returns exhibit pronounced long-term memory. This “stylized fact” can shed further insight on price dynamics that might be used for risk estimation. We also studied the sharp fluctuation of stock price index in Chinese stock market using multifractal spectrum and multifractal detrended fluctuation analysis (MF-DFA), respectively, and found that when the stock price index fluctuates sharply, a strong variability is clearly characterized by multifractal parameters and the generalized Hurst exponents [3] and [4]. Zhang et al. [5] tried to capture the fluctuations caused by the extreme event on crude oil prices variation during the analyzed period using an empirical mode decomposition (EMD-based) event analysis approach. It was found that this method provided a feasible solution to estimate the impact of extreme events on crude oil prices variation. In addition, many relative researches have been performed in order to capture the main features of extreme fluctuations [6], [7], [8], [9], [10], [11] and [12], all of these results are meaningful and important and can lead to a better understanding of complex stock markets. However, it is noted that most of the previous researches concentrated on the time series analysis of capital price series and capturing the statistical characteristics of financial time series, and few focused on the temporal dynamics of financial sharp fluctuation (or extreme fluctuation) sequences. In fact, the temporal dynamics of sharp fluctuation sequences are very useful information for understanding possible causes of sharp fluctuation, improving sharp fluctuation prediction and financial risk management as well as for improving predictive models. Nevertheless, the temporal dynamics of sharp fluctuation are still seldom known because the dynamics of sharp fluctuation result from many complex interaction factors and also factors involving human activities. It is very important and meaningful to study the temporal behavior and dynamics characteristics of sharp fluctuation of financial markets. Therefore, a further research work will help us to get a better understanding of the nature of stock price dynamics. On the other hand, Telesca et al. [13], [14], [15], [16], [17], [18], [19], [20], [21] and [22] studied the characterization of temporal fluctuations in other complex systems, such as seismic sequences, car accident sequence and forest fire sequence, etc. The fundamental principle of these researches is that extreme event sequence can be assumed to be a realization of a point process. The discrete-time process can be derived from the stochastic point process in two equivalent ways (1) using the inter-event time series or (2) forming its relative counting process. In the first representation a discrete-time series is formed by the rule τi = ti+1 − ti, where ti indicates the time of event numbered by the index i. In the second representation, the time axis is divided into equally spaced contiguous counting windows of duration T. The duration T of the window is called counting time or timescale. The latter approach considers the extreme events as the events of interest and assumes that there is an objective clock for the timing of the events. The former approach emphasizes the interspike intervals and uses the event number as an index of the time [16] and [17]. This research idea can also be applied in the temporal fluctuation analysis on sharp fluctuation in stock markets, for sharp fluctuation (or extreme fluctuation) sequences can also be viewed as a realization of a stochastic point process. In this context, our study aims to analyze the time-clustering characteristics of sharp fluctuation sequences of stock markets in China. We performed a detailed statistical analysis to investigate the time-clustering properties of the sharp fluctuation sequences of stock markets in China. The statistical tools include coefficient of variation, Allan Factor, Fano Factor as well as R/S (rescaled range) analysis. All of these empirical results suggest that the sequences are characterized by a high degree of time-clusterization. It can help us to get a better understanding of the nature and dynamics of sharp fluctuation of stock price in stock markets.

Using two different representations of the sharp fluctuations (inter-event times and series of counts), the time clustering behavior in the sharp fluctuation sequences of stock markets in China is studied. All of empirical results demonstrate that the sharp fluctuation sequences in Chinese stock markets are characterized by a time-clustering behavior and show long-range correlation. The characterization of time clustering in sharp fluctuation sequences provides valuable information to better understand the sharp fluctuation behavior. However, the potential of time dynamical features of sharp fluctuation (especially extreme fluctuation) sequences is far from being fully exploited. How to deeply understand the essence of the time-clustering behavior and long memory effects in capital markets and how to reveal more valuable information about market changes, furthermore, how to use information on these features in risk management, are key issues in the future. Research on these issues will help to make more accurate risk estimation and suggest effective measures for risk prevention and control in stock market.