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Register a new userScaling and memory of intraday volatility return intervals in stock market
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We study the return interval $tau$ between price volatilities that are above a certain threshold $q$ for 31 intraday datasets, including the Standard & Poors 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold $q$, the probability density function $P_q(tau)$ scales with the mean interval $bar{tau}$ as $P_q(tau)={bar{tau}}^{-1}f(tau/bar{tau})$, similar to that found in daily volatilities. Since the intraday records have significantly more data points compared to the daily records, we could probe for much higher thresholds $q$ and still obtain good statistics. We find that the scaling function $f(x)$ is consistent for all 31 intraday datasets in various time resolutions, and the function is well approximated by the stretched exponential, $f(x)sim e^{-a x^gamma}$, with $gamma=0.38pm 0.05$ and $a=3.9pm 0.5$, which indicates the existence of correlations. We analyze the conditional probability distribution $P_q(tau|tau_0)$ for $tau$ following a certain interval $tau_0$, and find $P_q(tau|tau_0)$ depends on $tau_0$, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval $<tau|tau_0>$ increases with $tau_0$, consistent with the memory found for $P_q(tau|tau_0)$. Moreover, we find that return interval records have long term correlations with correlation exponents similar to that of volatility records.
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We investigate the probability distribution of the volatility return intervals $tau$ for the Chinese stock market. We rescale both the probability distribution $P_{q}(tau)$ and the volatility return intervals $tau$ as $P_{q}(tau)=1/bar{tau} f(tau/bar{tau})$ to obtain a uniform scaling curve for different threshold value $q$. The scaling curve can be well fitted by the stretched exponential function $f(x) sim e^{-alpha x^{gamma}}$, which suggests memory exists in $tau$. To demonstrate the memory effect, we investigate the conditional probability distribution $P_{q} (tau|tau_{0})$, the mean conditional interval $<tau|tau_{0}>$ and the cumulative probability distribution of the cluster size of $tau$. The results show clear clustering effect. We further investigate the persistence probability distribution $P_{pm}(t)$ 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 $tau$. The scaling and long memory effect of $tau$ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.
Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the S&P 500, FTSE100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TARCH and EGARCH. We also test for asymmetry after controlling for the effect of macroeconomic factors on stock market returns using TAR and M-TAR specifications within a VAR framework. Our results show that the conditional variance is an asymmetric function of past innovations raising proportionately more during market declines, a phenomenon known as the leverage effect. However, when we control for the effect of changes in macroeconomic variables, we find no significant evidence of asymmetric behaviour of the stock market returns. There are some signs that the Portuguese Stock Market tends to show somewhat less market efficiency than other markets since the effect of the shocks appear to take a longer time to dissipate.
Summarized by the efficient market hypothesis, the idea that stock prices fully reflect all available information is always confronted with the behavior of real-world markets. While there is plenty of evidence indicating and quantifying the efficiency of stock markets, most studies assume this efficiency to be constant over time so that its dynamical and collective aspects remain poorly understood. Here we define the time-varying efficiency of stock markets by calculating the permutation entropy within sliding time-windows of log-returns of stock market indices. We show that major world stock markets can be hierarchically classified into several groups that display similar long-term efficiency profiles. However, we also show that efficiency ranks and clusters of markets with similar trends are only stable for a few months at a time. We thus propose a network representation of stock markets that aggregates their short-term efficiency patterns into a global and coherent picture. We find this financial network to be strongly entangled while also having a modular structure that consists of two distinct groups of stock markets. Our results suggest that stock market efficiency is a collective phenomenon that can drive its operation at a high level of informational efficiency, but also places the entire system under risk of failure.
We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold $q$ for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval $tau$ and its mean $<tau>$. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.
Geography effect is investigated for the Chinese stock market including the Shanghai and Shenzhen stock markets, based on the daily data of individual stocks. The Shanghai city and the Guangdong province can be identified in the stock geographical sector. By investigating a geographical correlation on a geographical parameter, the stock location is found to have an impact on the financial dynamics, except for the financial crisis time of the Shenzhen market. Stock distance effect is further studied, with a crossover behavior observed for the stock distance distribution. The probability of the short distance is much greater than that of the long distance. The average stock correlation is found to weakly decay with the stock distance for the Shanghai stock market, but stays nearly stable for different stock distance for the Shenzhen stock market.
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