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 r c . Through an exponential bin plot, we observe that the quiet-time distribution (qtd) shows power-law behavior, p f ( t ) ∼ t - β , for a range of threshold values. The quiet-time distribution has two scaling regimes, separated by the crossover time t c ≈ 200 min . The power-law exponents of the quiet-time distribution decrease when the return time Δ t increases. In the late-time regime, t > t c , 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 p f ( t ) ∼ ( 1 / T ) f ( t / T ) where the scaling function f ( x ) ∼ x - β 2 and T is the average quiet time. The scaling exponents β 2 depend on the return time Δ t and are independent of the threshold r c . The average quiet time follows the power law such as T ∼ r c δ where the exponents δ depend on the return time Δ t .