Modified Model of Multiplication Cascade Image-Based 2D MF-DFA with Sign Retention

In this paper, we propose a two-dimensional multifractal sign retention detrending fluctuation analysis algorithm (2D MF-S-DFA), which takes the sign of the residual matrix into account when calculating the detrending fluctuation function in traditional 2D MF-DFA. We evaluate these two methods based on images constructed from p-model multiplicative cascades. The results indicate that the numerical solution of the images extracted by 2D MF-S-DFA is closer to the theoretical solution of the multiplicative cascade images. In addition, we also compare the performance of the two methods after transforming the important parameters of the multiplicative cascade images. The results show that the relative errors and overall distance between the generalized Hurst exponent H(q) and the scale exponent tau(q) extracted by 2D MF-S-DFA and the image feature values are smaller than those of 2D MF-DFA. We can conclude that the sign retention algorithm outperforms the traditional 2D MF-DFA.