Modified multifractal large deviation spectrum based on CID for financial market system

Abstract

We modify the basic roughness grain exponent, only available for application of one single series, to complexity-invariant distance (CID) for studying multifractal features between two time series. CID is taken into consideration as a new roughness grain exponent with the large deviation spectrum to detect the similarity and correlation between different stock markets in this work.The new method is firstly applied to artificial series in order to test the scale invariance hypothesis with both the Legendre spectrum and large deviation spectrum. Results show that the large deviation spectrum is better in the detection of multifractal analysis between two time series as it exhibit plentiful scaling structures. Then we investigate the scaling behavior between financial time series so as to test whether there is scale invariance of stock markets in China and the US. Besides, from the α values responding to the maximal fα in the 5 pair series and the widths of the spectrum, a new way of measurement of the similarity and correlation has been found. To overcome the limitation of q, we then compute the surface area of the large deviation spectrum under each scale and further detect the evolution of the slope by a scaling/non-scaling criterion which helps in the measurement of scaling behavior. Moreover, the proposed method can give us more information between different markets and distinguish them from different angles.