TESTING FOR EFFECTS OF CROSS-CORRELATIONS ON JOINT MULTIFRACTALITY

Abstract

Joint multifractality has been studied in many areas of applied sciences, but few studies focused on the sources of joint multifractality, especially the cross-correlations between two records which play a crucial role in the presence of joint multifractality. To test the effect of cross-correlations on joint multifractality, we propose a de-cross-correlation method via the shifting technique based on the framework of multifractal detrended cross-correlation analysis (MF-DCCA), namely, multifractal detrended de-cross-correlation analysis (MF-DDA). It keeps the original detrending procedure of MF-DCCA. The proposed method is validated via some simulation and real data including multifractal random walk (MRW), daily water levels, and daily stock returns. Results of validation show that the MF-DDA can detect the effects of cross-correlations between simulation series and between real series, and are consistent with the simulation setting of MRW and the actual situation of real data. This proposed method can be extended to other similar joint multifractal analysis methods.