The study of the relationship between the concentration of PM_2.5 and the local air quality index (AQI) is significant for the improvement of urban air quality. This study not only considered multifractal cross-correlation but also the fluctuation conduction mechanism. An asymmetric multifractal detrended cross-correlation analysis (MF-DCCA) method based on fluctuation conduction is introduced here to empirically explore the causality and conduction time between air quality factors and PM_2.5 concentration. The empirical results indicate the existence of a bidirectional fluctuation conduction effect between PM_2.5 and PM₁₀, SO₂, and NO₂ in Hangzhou, China, with a conduction time of 30 hours; this effect is non-existent between PM_2.5 and O₃. In addition, there is a unidirectional fractal fluctuation conduction between PM_2.5 and CO with a conduction time of 21 hours.

1. [1] R. T. Vassoler and G. F. Zebende, “DCCA cross-correlation coefficient apply in time series of air temperature and air relative humidity,” Physica A: Statistical Mechanics and its Applications, Vol.391, Issue 7, pp. 2438-2443, 2012.
2. [2] D. D. Kang, D. I. Lee, B.-H. Kwon, K. Kim, and J.-K. Park, “Features of the detrended cross-correlation analysis in the time series between absorbable particulate matter and meteorological factors,” J. of the Korean Physical Society, Vol.63, Issue 1, pp. 10-17, 2013.
3. [3] S. Hajian and M. S. Movahed, “Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations,” Physica A: Statistical Mechanics and its Applications, Vol.389, Issue 21, pp. 4942-4957, 2010.
4. [4] K. Shi, “Detrended cross-correlation analysis of temperature, rainfall, PM₁₀ and ambient dioxins in Hong Kong,” Atmospheric Environment, Vol.97, pp. 130-135, 2014.
5. [5] C. Shen, C. Li, and Y. Si, “A detrended cross-correlation analysis of meteorological and API data in Nanjing. China,” Physica A: Statistical Mechanics and its Applications, Vol.419, pp. 417-428, 2015.
6. [6] G. Cao, Y. Han, Q. Li, and W. Xu, “Asymmetric MF-DCCA method based on risk conduction and its application in the Chinese and foreign stock markets,” Physica A: Statistical Mechanics and its Applications, Vol.468, pp. 119-130, 2017.
7. [7] E. Baek and W. Brock, “A general test for non-linear Granger causality: bivariate model,” Working Paper, Iowa State University and University of Wisconsin–Madison, 1992.
8. [8] C. Hiemstra and J. D. Jones, “Testing for Linear and Nonlinear Granger Causality in the Stock Price-Volume Relation,” The J. of Finance, Vol.49, Issue 5, pp. 1639-1664, 1994.