Statistical properties of daily ensemble variables in the Chinese stock markets

Gu, Gao-Feng; Zhou, Wei‐Xing

doi:10.1016/j.physa.2007.05.007

Cited by 22 publications

(12 citation statements)

References 47 publications

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“…However, the exponents of Shanghai Index are similar with those of the United States[2]. (iii) Our results are compatible with those in Refs [22,20,30]…”

supporting

confidence: 91%

“…This method has now been accepted as one of the standard methods to measure multifractality, and has extensively been used since it came into being. Based on the MFDFA and modified R/S analysis, Gu and Zhou [20] study dynamical behavior of the Chinese stock market by investigating the statistical properties. Jiang and Zhou [21] apply the partition function approach and find that the Chinese stock market also exhibited multifractal behavior as a whole.…”

Section: Introductionmentioning

confidence: 99%

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Power law and multiscaling properties of the Chinese stock market

Bai

Zhu

2010

Physica A: Statistical Mechanics and its Applications

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“…However, the exponents of Shanghai Index are similar with those of the United States[2]. (iii) Our results are compatible with those in Refs [22,20,30]…”

supporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Power law and multiscaling properties of the Chinese stock market

Bai

Zhu

2010

Physica A: Statistical Mechanics and its Applications

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“…This surprising behavior of the stock markets led the authors to formulate the so-called “inverse cubic law”—a conjecture that the power-law tails of the return distributions with the scaling exponent

are a universal property of all stock markets at short and medium time scales [ 18 ]. Indeed, similar statistical characteristics were found by other researchers in data collected from other stock markets [ 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ], Forex [ 36 ], commodity markets [ 36 , 37 ], and the cryptocurrency market [ 36 , 38 , 39 , 40 ].…”

Section: Introductionsupporting

confidence: 83%

Financial Return Distributions: Past, Present, and COVID-19

Wątorek

Kwapień

Dróżdż

2021

Entropy

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We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.

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“…Mandelbrot and Wallis argued that this phenomenon is a characteristic of a time series with a large cyclic component. This slope variation was also discussed for the ensemble returns of individual stocks in SHSE [24]. Details of the cyclic trend is beyond the scope of the current paper and will be discussed elsewhere.…”

Section: The Modified R/s Statisticmentioning

confidence: 88%

“…Chinese stock markets are emerging markets, and a few papers have studied their distributions and specifications of returns of stocks and indices [18−23]. Specifically, Gu and Zhou [24] found evidence of long-term memory in the ensemble daily price returns within several time periods of 500 stocks traded in the Shanghai Stock Exchange by using the detrended fluctuation analysis, the R/S analysis, and the MRS analysis. Moreover, there are quite a few other papers [25−27] which have applied the generalized spectral derivative method [28] to the Chinese stock markets to demonstrate that Chinese stock markets are far from being weak in terms of market efficiency.…”

mentioning

confidence: 99%

Long-term memory of the returns in the Chinese stock indices

Wan

Zhang

2008

Front. Phys. China

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The modified R/S statistic (MRS) and the local Whittle method (LWM) are used to analyze the long-range dependence on various indices of the Chinese stock markets. The MRS accepts the null hypothesis of no long-range dependence while the LWM rejects it. We also find that the long-range dependence phenomena presented in these markets depend on the time in which they are measured. Keywords long-range dependence, modified R/S statistic, local Whittle estimator PACS numbers 89.65.Gh, 05.45.Tp, 02.50.-r ½ ÁÒØÖÓ Ù Ø ÓÒLong-range dependence, also commonly referred to as long-term memory or correlation, has a long history and remains an active topic of research in the study of financial time series. A lot of empirical studies have been done on the long-range dependence of stock markets. In 1970s Mandelbrot [1−3] introduced the rescaled range statistic (R/S) method, which was originally invented by Hurst [4], to evaluate the Hurst exponent H in analyzing the long-term memory of security returns, and found that it was quite larger than 1/2 for stock prices and returns of interest rates. It displays a strong positive long-range correlation, and challenges the efficient market hypothesis and the related random walk model. A clear description of these issues can be found in Ref. [5]. Similar results were also obtained by Greene and Fielitz [6]. As we know, many other financial variables (such as volatility, trade sign, et al.) possess long-term memory, which are less debated. However, there is a tremendous discord between affirmation and denial of the long-term memory for security returns. In 1988 Fama and French [7] argued that the long-range dependence of stock returns is weak for weekly and daily data, and returns for a longer time have a negative correlation. Aydogan and Booth [8] believed that no long-term dependence exists in stock returns. In 1991 Lo [9] declared that the classical R/S analysis is sensitive to the presence of short-range dependencies. Evidence of dependence using the classical R/S statistic may come merely from short-range dependencies instead of long-range ones. He proposed a modified R/S (MRS) statistic to determine the long-term memory. Nevertheless, some economists said that an acceptance of the null hypothesis of no long-range dependence based on the MRS statistic should never be viewed as the "final word". Teverovsky, Taqqu and Willinger [10] identified a number of problems associated with Lo's method and its use in practice. They verified that Lo's MRS statistic has a strong preference for accepting the null hypothesis of no long-range dependence.Another widely used methodology, called the Whittle estimator, evaluates the long-term memory parameter through the log-periodogram regression estimator proposed by Geweke and Porter-Hudak [11]. Unlike the MRS, this method is frequency-domain based and applies maximum likelihood techniques. However, it has been criticized because of its finite-sample bias. Robinson [12] proposed a least biased semi-parametric estima-

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Statistical properties of daily ensemble variables in the Chinese stock markets

Cited by 22 publications

References 47 publications

Power law and multiscaling properties of the Chinese stock market

Power law and multiscaling properties of the Chinese stock market

Financial Return Distributions: Past, Present, and COVID-19

Long-term memory of the returns in the Chinese stock indices

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