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Detecting PM2.5’s Correlations between Neighboring Cities Using a Time-Lagged Cross-Correlation Coefficient

, 1 , 2 , 2 , 3

Scientific Reports

Nature Publishing Group UK

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      Abstract

      In order to investigate the time-dependent cross-correlations of fine particulate (PM2.5) series among neighboring cities in Northern China, in this paper, we propose a new cross-correlation coefficient, the time-lagged q-L dependent height crosscorrelation coefficient (denoted by p q(τ, L)), which incorporates the time-lag factor and the fluctuation amplitude information into the analogous height cross-correlation analysis coefficient. Numerical tests are performed to illustrate that the newly proposed coefficient ρ q(τ, L) can be used to detect cross-correlations between two series with time lags and to identify different range of fluctuations at which two series possess cross-correlations. Applying the new coefficient to analyze the time-dependent cross-correlations of PM2.5 series between Beijing and the three neighboring cities of Tianjin, Zhangjiakou, and Baoding, we find that time lags between the PM2.5 series with larger fluctuations are longer than those between PM2.5 series withsmaller fluctuations. Our analysis also shows that cross-correlations between the PM2.5 series of two neighboring cities are significant and the time lags between two PM2.5 series of neighboring cities are significantly non-zero. These findings providenew scientific support on the view that air pollution in neighboring cities can affect one another not simultaneously but with a time lag.

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        Multifractal detrended fluctuation analysis of nonstationary time series

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        We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series to those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima (WTMM) method, and show that the results are equivalent.
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          Air pollution in mega cities in China

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            Author and article information

            Affiliations
            [1 ]GRID grid.257160.7, College of Science/Agricultural Mathematical Modeling and Data Processing Center, Hunan Agricultural University, ; Changsha, P. R. China
            [2 ]ISNI 0000 0004 0402 6152, GRID grid.266820.8, Department of Mathematics and Statistics, University of New Brunswick, ; Fredericton, NB E3B 5A3 Canada
            [3 ]ISNI 0000 0001 1958 9263, GRID grid.268252.9, Department of Mathematics, Wilfrid Laurier University, ; Waterloo, ON N2L 3C5 Canada
            Contributors
            popwang619@163.com
            Journal
            Sci Rep
            Sci Rep
            Scientific Reports
            Nature Publishing Group UK (London )
            2045-2322
            31 August 2017
            31 August 2017
            2017
            : 7
            28860644
            5579243
            10419
            10.1038/s41598-017-10419-6
            © The Author(s) 2017

            Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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