Scaling and memory effect in volatility return interval of the Chinese stock market
01 Dec 2008-Physica A-statistical Mechanics and Its Applications (North-Holland)-Vol. 387, Iss: 27, pp 6812-6818
TL;DR: In this paper, Liu et al. investigated the probability distribution of the volatility return intervals τ for the Chinese stock market and showed that the scaling and long memory effect of τ are similar to those obtained from the United States and the Japanese financial markets.
Abstract: We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution P q ( τ ) and the volatility return intervals τ as P q ( τ ) = 1 / τ ¯ f ( τ / τ ¯ ) to obtain a uniform scaling curve for different threshold value q . The scaling curve can be well fitted by the stretched exponential function f ( x ) ∼ e − α x γ , which suggests memory exists in τ . To demonstrate the memory effect, we investigate the conditional probability distribution P q ( τ | τ 0 ) , the mean conditional interval 〈 τ | τ 0 〉 and the cumulative probability distribution of the cluster size of τ . The results show clear clustering effect. We further investigate the persistence probability distribution P ± ( t ) and find that P − ( t ) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ . The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.
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TL;DR: In this article, the long memory property in the volatility of Chinese stock markets is examined for this purpose, and two semi-parametric tests (GPH and LW) and the FIGARCH model were applied to four Chinese market indices: Shanghai A, Shanghai B, Shenzhen A and Shenzhen B.
Abstract: In this study, the long memory property in the volatility of Chinese stock markets is examined For this purpose, we applied two semi-parametric tests (GPH and LW) and the FIGARCH model, to four Chinese market indices: Shanghai A, Shanghai B, Shenzhen A and Shenzhen B From the results of our analysis, we can conclude that the volatility of Chinese stock markets exhibits long memory features, and that the assumption of non-normality provides better specifications regarding long memory volatility processes
65 citations
Cites background from "Scaling and memory effect in volati..."
...For example, the scaling behavior and long range correlations are statistically discovered in stock returns, intertrade durations and the trading volume in the Chinese stock market [29–33]....
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TL;DR: In this article, the probability distributions of the recurrence intervals τ between consecutive 1-min returns above a positive threshold q>0 or below a negative threshold q <0 of two indices and 20 individual stocks in China's stock market were investigated.
Abstract: We investigate the probability distributions of the recurrence intervals τ between consecutive 1-min returns above a positive threshold q>0 or below a negative threshold q<0 of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresholds are symmetric, and display power-law tails tested by three goodness-of-fit measures, including the Kolmogorov–Smirnov (KS) statistic, the weighted KS statistic and the Cramer–von Mises criterion. Both long-term and shot-term memory effects are observed in the recurrence intervals for positive and negative thresholds q. We further apply the recurrence interval analysis to the risk estimation for the Chinese stock markets based on the probability Wq(Δt,t), value-at-risk (VaR) analysis and VaR analysis conditioned on preceding recurrence intervals.
43 citations
TL;DR: The statistical properties of the return intervals τ q between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied in this paper, where the Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τ q for different thresholds q. Furthermore, the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function f ( τ / τ ) ∼ e − α ( τ/ τ ) γ with γ ≈
Abstract: The statistical properties of the return intervals τ q between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied. The Kolmogorov–Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τ q for different thresholds q . Furthermore, the KS test and weighted KS test show that the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function f ( τ / τ ) ∼ e − α ( τ / τ ) γ with γ ≈ 0.31 under the significance level of 5%, where τ is the mean return interval. The investigation of the conditional probability distribution P q ( τ | τ 0 ) and the mean conditional return interval 〈 τ | τ 0 〉 demonstrates the existence of short-term correlation between successive return interval intervals. We further study the mean return interval 〈 τ | τ 0 〉 after a cluster of n intervals and the fluctuation F ( l ) using detrended fluctuation analysis, and find that long-term memory also exists in the volatility return intervals.
42 citations
TL;DR: In this paper, the cumulative distribution of trading volume is investigated for Chinese stocks, and the distribution is well fitted by a stretched exponential function f(x)∼e−αxγ.
Abstract: The cumulative distribution of trading volume is investigated for Chinese stocks. Different from the power-law scaling of mature markets, the distribution is well fitted by a stretched exponential function f(x)∼e−αxγ. With the autocorrelation function and the detrended fluctuation analysis, the long-range autocorrelation of trading volume is revealed. The conditional dependence of volume on volatility and the volume–volatility cross-correlation are studied, and a positive long-range correlation between volume and volatility is observed.
40 citations
TL;DR: In this article, the authors investigated the statistical properties of the recurrence intervals of daily volatility time series of four NYMEX energy futures, defined as the waiting times τ between consecutive volatilities exceeding a given threshold q.
37 citations
References
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TL;DR: This work analyzes two classes of controls consisting of patchy nucleotide sequences generated by different algorithms--one without and one with long-range power-law correlations, finding that both types of sequences are quantitatively distinguishable by an alternative fluctuation analysis method.
Abstract: Long-range power-law correlations have been reported recently for DNA sequences containing noncoding regions We address the question of whether such correlations may be a trivial consequence of the known mosaic structure ("patchiness") of DNA We analyze two classes of controls consisting of patchy nucleotide sequences generated by different algorithms--one without and one with long-range power-law correlations Although both types of sequences are highly heterogenous, they are quantitatively distinguishable by an alternative fluctuation analysis method that differentiates local patchiness from long-range correlations Application of this analysis to selected DNA sequences demonstrates that patchiness is not sufficient to account for long-range correlation properties
4,365 citations
TL;DR: A new method--detrended fluctuation analysis (DFA)--for quantifying this correlation property in non-stationary physiological time series is described and application of this technique shows evidence for a crossover phenomenon associated with a change in short and long-range scaling exponents.
Abstract: The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state [Physiol. Rev. 9, 399-431 (1929)]. However, recent studies [Phys. Rev. Lett. 70, 1343-1346 (1993); Fractals in Biology and Medicine (Birkhauser-Verlag, Basel, 1994), pp. 55-65] reveal that under normal conditions, beat-to-beat fluctuations in heart rate display the kind of long-range correlations typically exhibited by dynamical systems far from equilibrium [Phys. Rev. Lett. 59, 381-384 (1987)]. In contrast, heart rate time series from patients with severe congestive heart failure show a breakdown of this long-range correlation behavior. We describe a new method--detrended fluctuation analysis (DFA)--for quantifying this correlation property in non-stationary physiological time series. Application of this technique shows evidence for a crossover phenomenon associated with a change in short and long-range scaling exponents. This method may be of use in distinguishing healthy from pathologic data sets based on differences in these scaling properties.
3,411 citations
Book•
01 Jan 2001TL;DR: In this article, first passage in an interval is illustrated in simple geometries, and the first passage is in a semi-infinite system and a non-fractal system.
Abstract: Preface Errata 1. First-passage fundamentals 2. First passage in an interval 3. Semi-infinite system 4. Illustrations of first passage in simple geometries 5. Fractal and nonfractal networks 6. Systems with spherical symmetry 7. Wedge domains 8. Applications to simple reactions References Index.
1,891 citations
"Scaling and memory effect in volati..." refers background in this paper
...ase ordering dynamics and critical dynamics [18, 19, 20, 21, 22]. The idea of persistence is closely related to the first passage time which has been widely studied in physics, biology and engineering [23, 24, 25, 26, 27]. In general, the persistence probability provides additional information to the autocorrelation. The persistence probability P +(t)(P−(t)) is defined as the probability that τ(t′ +et) has always been ...
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TL;DR: In this paper, it was shown that the scaling of the probability distribution of a particular economic index can be described by a non-gaussian process with dynamics that, for the central part of the distribution, correspond to that predicted for a Levy stable process.
Abstract: THE large-scale dynamical properties of some physical systems depend on the dynamical evolution of a large number of nonlinearly coupled subsystems. Examples include systems that exhibit self-organized criticality1 and turbulence2,3. Such systems tend to exhibit spatial and temporal scaling behaviour–power–law behaviour of a particular observable. Scaling is found in a wide range of systems, from geophysical4 to biological5. Here we explore the possibility that scaling phenomena occur in economic systemsa-especially when the economic system is one subject to precise rules, as is the case in financial markets6–8. Specifically, we show that the scaling of the probability distribution of a particular economic index–the Standard & Poor's 500–can be described by a non-gaussian process with dynamics that, for the central part of the distribution, correspond to that predicted for a Levy stable process9–11. Scaling behaviour is observed for time intervals spanning three orders of magnitude, from 1,000 min to 1 min, the latter being close to the minimum time necessary to perform a trading transaction in a financial market. In the tails of the distribution the fall-off deviates from that for a Levy stable process and is approximately exponential, ensuring that (as one would expect for a price difference distribution) the variance of the distribution is finite. The scaling exponent is remarkably constant over the six-year period (1984-89) of our data. This dynamical behaviour of the economic index should provide a framework within which to develop economic models.
1,689 citations
01 Oct 2001
TL;DR: In this paper, first passage in an interval is illustrated in simple geometries, and the first passage is in a semi-infinite system and a non-fractal system.
Abstract: Preface Errata 1. First-passage fundamentals 2. First passage in an interval 3. Semi-infinite system 4. Illustrations of first passage in simple geometries 5. Fractal and nonfractal networks 6. Systems with spherical symmetry 7. Wedge domains 8. Applications to simple reactions References Index.
1,282 citations