Testing For The Source Of Joint Multifractality

Joint multifractality is used to describe the nonlinear correlation within and between sequences.For single multifractals,two causes are known as follows :(1)The probability distribution of the original sequence is thick-tailed;(2)Autocorrelation of the original sequence.But for joint multifractality,the crosscorrelation between sequences will also affect the joint multifractal characteristics.Therefore,the cause test for joint multifractality needs to be expanded on the basis of the single multifractality test.Based on the study of joint multifractality,this paper proposes a hypothesis testing method for the cause of joint multifractality and Multifractal Detrended De-cross-correlation method(MF-DDA)to test the influence of cross-correlation between sequences on joint multifractality,and judges whether the proposed method is effective through numerical and empirical analysis.Firstly,a joint multifractal cause hypothesis test method is established.In this method,two pairs of substitution sequences are constructed.Each substitution sequence destroys one of the causes while retaining the other.Using the joint multifractal analysis method: Multifractal Detrending Cross-correlation method(MF-DCCA)is applied to the substitution sequence to obtain the generalized Hurst exponent and generate the test interval of hypothesis test.The generalized Hurst exponent of the original sequence is also calculated by the MF-DCCA method,and whether it falls within the acceptance domain,and thus accepts or rejects the null hypothesis.Then the Multifractal Detrended De-cross-correlation method(MF-DDA)is proposed.This method not only keeps the good performance of MF-DCCA method,but also uses the displacement technology to shift the segmented cells to destroy the cross-correlation of sequences to the maximum extent without changing the autocorrelation of sequences,so as to verify the cross-correlation between sequences is one of the important causes of joint multifractality.Finally,the effectiveness of the combined multiple factorial hypothesis test method and MF-DDA method is verified.In this paper,three sets of data are used respectively for numerical analysis and empirical analysis:(1)Simulation data: two groups of multifractal random walk(MRW)with obvious strong and weak cross-correlation;(2)River water level data observed every six minutes by 10 observation stations in northern China were paired with stations at adjacent locations to form nine pairs of data;(3)The daily stock return series of eight enterprises in the A stock market,and the data are pared according to the strength of the correlation between enterprises to form four pairs of matching data.Finally,we can draw the following conclusions:(1)the joint multifractal causation hypothesis test method can test the thick tail characteristics of the probability distribution of the original sequence and the correlation within or between the original sequence is the cause of joint multifractal;(2)The use of MFDDA method can effectively destroy the cross-correlation between sequences.