A connectivity map of China based on the directional dependences between the four cities in the year 2013.

Base map figure source: CIA Maps (https://www.cia.gov/library/publications/resources/cia-maps-publications/China.html).</p

Scatterplot matrix for daily time series data of the PM2.5 levels between the four Chinese cities (BJ: Beijing, CD: Chengdu, GZ: Guangzhou, SH: Shanghai) during the year 2013.

Scatterplot matrix for daily time series data of the PM2.5 levels between the four Chinese cities (BJ: Beijing, CD: Chengdu, GZ: Guangzhou, SH: Shanghai) during the year 2013.</p

Time series data of PM2.5 levels in the four Chinese cities (Beijing, Chengdu, Guangzhou, and Shanghai) during the year 2013.

Time series data of PM2.5 levels in the four Chinese cities (Beijing, Chengdu, Guangzhou, and Shanghai) during the year 2013.</p

Spearman correlation coefficients of daily maximums of the PM2.5 levels between each pair of the four Chinese cities (BJ: Beijing, CD: Chengdu, GZ: Guangzhou, SH: Shanghai) during the years 2013 to 2017.

Spearman correlation coefficients of daily maximums of the PM2.5 levels between each pair of the four Chinese cities (BJ: Beijing, CD: Chengdu, GZ: Guangzhou, SH: Shanghai) during the years 2013 to 2017.</p

A connectivity map of China based on the directional dependences between the four cities in the year 2016.

Base map figure source: CIA Maps (https://www.cia.gov/library/publications/resources/cia-maps-publications/China.html).</p

Histograms of PM2.5 levels in the four Chinese cities during the year 2013.

Histograms of PM2.5 levels in the four Chinese cities during the year 2013.</p

Predicted values (black straight line) of PM2.5 levels of the four Chinese cities during the year 2013 and the observed PM2.5 measurements (red dotted line).

Predicted values (black straight line) of PM2.5 levels of the four Chinese cities during the year 2013 and the observed PM2.5 measurements (red dotted line).</p

Details on the feedforward neural networks used for autocorrelation estimation.

L: the number of input nodes, i.e., the lag order, H: the number of nodes in the hidden layer.</p

Copula directional dependences (CDDs) between ordered pairs of Chinese cities (BJ: Beijing, CD: Chengdu, GZ: Guangzhou, SH: Shanghai) during the years 2013 to 2017, together with 95% bootstrap confidence intervals (CIs) for the difference of directional dependences.

The larger value between the two directional dependences is marked in bold font.</p

A connectivity map of China based on the directional dependences between the four cities in the year 2015.

Base map figure source: CIA Maps (https://www.cia.gov/library/publications/resources/cia-maps-publications/China.html).</p