Formation Mechanism of the Accumulative Magnification Effect in a Financial Time Series

Structural information contained in financial time series can be magnified effectively by constructing the accumulative return. In order to make the magnification effects of different financial time series comparative, we first propose a standard method to characterize the strength of the accumulative magnification effect. Then, we employ decomposed-randomized technology to uncover the formation mechanism of the accumulative magnification effect. Our results show that (1) the standard deviation pattern is determined by volatility dependence, (2) the Hurst exponent pattern is induced by sign dependence, (3) an approximate entropy pattern is caused by the combined effect of sign dependence and volatility dependence.