The persistence probability and the price–price correlation functions in the Korean stock market

Abstract

We consider the one minute time series of the Korean stock market index (KOSPI). We defined the persisting time as the time interval when the index remains above (or below) an initial index. We observed that the average persistence probability P ( t ) followed a power-law behavior like P ( t ) ∼ t − θ with the persistence exponent θ = 0.477 ( 2 ) . The persistence exponent in the Korean stock market deviates slightly from a random process. The Korean stock market has shown a weak anti-persistence. We measured the persistence properties of the stock market by the generalized price–price correlation function F q ( t ) . The price–price correlation function followed a power law, F q ( t ) ∼ t h q , where h q is called the generalized Hurst exponent. The generalized Hurst exponent depends on the order q which means that there are multiscaling properties in the time series of the stock index. We observed the relationship θ + h 2 = 1 between the error bars where h 2 is the fractal dimension of the time series.