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

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 tc≈200min. 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 T∼rcδ where the exponents δ depend on the return time Δt.

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