In this study, a wavelet denoising method is first used to eliminate the influence of noise. Then, an overlapping smooth window technique is introduced into the asymmetric multifractal detrended cross-correlation analysis method, which was combined with the multiscale multifractal analysis method, resulting in the proposed asymmetric multiscale multifractal detrended cross-correlation analysis method. This method not only remedies the pseudo-fluctuation defect of the traditional method, but also explores the asymmetric multifractal cross-correlation between China’s rebar futures and spot markets at different scales. The results show the existence of an asymmetric multifractal cross-correlation between rebar futures and spot markets with upward and downward trends at different scales. This cross-correlation is highly complex at the small-scale, and more pronounced when the futures market is in an uptrend.

1. [1] Y. Yao, “Empirical research of price discovery in China,” Master thesis, Southwest University, 2012.
2. [2] B. F. Shi, A. W. Li, and J. Wang, “Price discovery on Chinese rebar futures market,” Operations Research and Management Science, Vol.27, No.6, pp. 162-171, 2018.
3. [3] G. X. Cao, Y. Han, W. J. Cui, and Y. Guo, “Multifractal detrended cross-correlations between the CSI 300 index futures and the spot markets based on high-frequency data,” Physica A: Statistical Mechanics and its Applications, Vol.414, pp. 308-320, 2014.
4. [4] G. X. Cao and W. Xu, “Multifractal features of EUA and CER futures markets by using multifractal detrended fluctuation analysis based on empirical model decomposition,” Chaos Solitons & Fractals, Vol.83, pp. 212-222, 2016.
5. [5] Y. Lin, D. Y. Zhang, X. Wu, and R. Z. Yan, “A research of asymmetric multifractal correlation in energy futures markets,” Management Review, Vol.29, No.2, pp. 35-46, 2017.
6. [6] J. Gierałtowski, J. J. Żebrowski, and R. Baranowski, “Multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia,” Physical Review E, Vol.58, No.2, 021915, 2012.
7. [7] W. Shi, P. Shang, J. Wang, and A. Lin, “Multiscale multifractal detrended cross-correlation analysis of financial time series,” Physica A: Statistical Mechanics and its Applications, Vol.403, pp. 35-44, 2014.
8. [8] Q. J. Fan, “Asymmetric multiscale detrended fluctuation analysis of California electricity spot price,” Physica A: Statistical Mechanics and its Applications, Vol.442, pp. 252-260, 2016.
9. [9] X. N. Zhang, M. Zeng, and Q. H. Meng, “Asymmetric multiscale multifractal analysis of wind speed signals,” Int. J. of Modern Physics C, Vol.28, No.11, 1750137, 2017.
10. [10] Y. J. Yang, J. P. Li, and Y. M. Yang, “The cross-correlation analysis of multi property of stock markets based on MM-DFA,” Physica A: Statistical Mechanics and its Applications, Vol.481, pp. 23-33, 2017.
11. [11] F. Wang, Q. J. Fan, and K. H. Wang, “Asymmetric multiscale multifractal detrended cross-correlation analysis for the 1999–2000 California electricity market,” Nonlinear Dynamics, Vol.91, No.3, pp. 1527-1540, 2018.
12. [12] G. X. Cao, J. Cao, and L. B. Xu, “Detrended cross-correlation analysis approach for assessing asymmetric multifractal detrended cross-correlations and their application to the Chinese financial market,” Physica A: Statistical Mechanics and its Applications, Vol.393, pp. 460-469, 2014.
13. [13] H. Zheng and B. H. Wang, “MultiFractal Empirical Study of Sino-Japanese Gold Futures Market: Based on OSW-MF-DFA Method. China,” Forward Position or Economics, No.11, pp. 35-43, 2009.
14. [14] P. F. Zhu and Y. Tang, “The Current Arbitrage Strategy From The Perspective of Fractals: Empirical Evidence Based on The Data of Stock Disaster,” Statistics and Decision, No.3, pp. 167-169, 2019.