# Power law of quiet time distribution in the Korean stock-market

**ABSTRACT** We report the quiet-time probability distribution of the absolute return in the Korean stock-market index. We define the quiet time as a time interval during the absolute return of the stock index that are above a threshold rc. Through an exponential bin plot, we observe that the quiet-time distribution (qtd) shows power-law behavior, pf(t)∼t-β, for a range of threshold values. The quiet-time distribution has two scaling regimes, separated by the crossover time . The power-law exponents of the quiet-time distribution decrease when the return time Δt increases. In the late-time regime, t>tc, the power-law exponents are independent of the threshold within the error bars for the fixed return time. The scaled qtd is characterized by a scaling function such as pf(t)∼(1/T)f(t/T) where the scaling function f(x)∼x-β2 and T is the average quiet time. The scaling exponents β2 depend on the return time Δt and are independent of the threshold rc. The average quiet time follows the power law such as where the exponents δ depend on the return time Δt.

- [Show abstract] [Hide abstract]

**ABSTRACT:**Previous work [Y. Zhang, M.M. Meerschaert, B. Baeumer, Particle tracking for time-fractional diffusion, Phys. Rev. E 78 (2008) 036705] showed how to solve time-fractional diffusion equations by particle tracking. This paper extends the method to the case where the order of the fractional time derivative is greater than one. A subordination approach treats the fractional time derivative as a random time change of the corresponding Cauchy problem, with a first derivative in time. One novel feature of the time-fractional case of order greater than one is the appearance of clustering in the operational time subordinator, which is non-Markovian. Solutions to the time-fractional equation are probability densities of the underlying stochastic process. The process models movement of individual particles. The evolution of an individual particle in both space and time is captured in a pair of stochastic differential equations, or Langevin equations. Monte Carlo simulation yields particle location, and the ensemble density approximates the solution to the variable coefficient time-fractional diffusion equation in one or several spatial dimensions. The particle tracking code is validated against inverse transform solutions in the simplest cases. Further applications solve model equations for fracture flow, and upscaling flow in complex heterogeneous porous media. These variable coefficient time-fractional partial differential equations in several dimensions are not amenable to solution by any alternative method, so that the grid-free particle tracking approach presented here is uniquely appropriate.Computers & Mathematics with Applications 02/2010; 59(3):1078-1086. DOI:10.1016/j.camwa.2009.05.009 · 2.00 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider the probability distribution function (pdf) and the multiscaling properties of the index and the traded volume in the Korean stock market. We observed the power law of the pdf at the fat tail region for the return, volatility, the traded volume, and changes of the traded volume. We also investigate the multifractality in the Korean stock market. We consider the multifractality by the detrended fluctuation analysis (MFDFA). We observed the multiscaling behaviors for index, return, traded volume, and the changes of the traded volume. We apply MFDFA method for the randomly shuffled time series to observe the effects of the autocorrelations. The multifractality is strongly originated from the long time correlations of the time series.Physica A: Statistical Mechanics and its Applications 09/2007; 383(1):65-70. DOI:10.1016/j.physa.2007.04.112 · 1.72 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider the probability distribution function of the trading volume and the volume changes in the Korean stock market. The probability distribution function of the trading volume shows double peaks and follows a power law, P(V/〈V〉)∼(V/〈V〉)−α at the tail part of the distribution with α=4.15(4) for the KOSPI (Korea composite Stock Price Index) and α=4.22(2) for the KOSDAQ (Korea Securities Dealers Automated Quotations), where V is the trading volume and 〈V〉 is the monthly average value of the trading volume. The second peaks originate from the increasing trends of the average volume. The probability distribution function of the volume changes also follows a power law, P(Vr)∼Vr−β, where Vr=V(t)−V(t−T) and T is a time lag. The exponents β depend on the time lag T. We observe that the exponents β for the KOSDAQ are larger than those for the KOSPI.Physica A: Statistical Mechanics and its Applications 03/2009; 388(6):863-868. DOI:10.1016/j.physa.2008.11.029 · 1.72 Impact Factor