## 2 Methods  
### Data  
South Korea began opening limited air pollution data of 16 stations to the public in 2002, and later expanded to providing real-time concentrations of six air pollutants from a well-constructed nationwide monitoring network consisting of 344 stations via a website ([[http://www.airkorea.or.kr](http://www.airkorea.or.kr)]([http://www.airkorea.or.kr](http://www.airkorea.or.kr))) in 2005. The dataset is composed of PM\({}_{2.5}\) mass concentrations recorded hourly from about 344 monitoring stations located nationwide in Korea, from 1 January 2015 to 31 December 2017. Most datasets contain erroneous data points due to operational errors of measuring devices and abnormal values. Thus, the authors selected datasets with less than 10% of missing data points during the whole time span. Finally, they obtained daily average concentrations with a total of 1090 data points each at 18 stations, which were categorized into urban and roadside groups. In fact, all monitoring stations were grouped into four categories: urban, suburban, roadside, and country background. However, most datasets were removed upon processing the wrong data points contained in the original time series. In this study, we analyze the daily average mass concentration of PM\({}_{2.5}\), defined as the daily average mass concentration instead of the logarithmic value, because the mass concentration is not stored and updated every hour.  
As shown in Figure 1, we can observe a seasonal trend as reported in other studies, i.e., a high concentration in the winter and spring, and a low concentration in the summer and fall. This trend shows a similar behavior to meteorological factors such as temperature, relative humidity, wind speed, air pressure, and precipitation. While there seems to be a strong dependence of PM\({}_{2.5}\) concentrations on meteorological factors, it is not clear whether there is a reliable causal relationship between them. No meteorological factor is determined to contribute to the concentration other than sharing a seasonal trend [7].  
Figure 2 shows the spatial variations in PM\({}_{2.5}\) concentrations. In particular, stations #15 and #18 show a low-level concentration, while stations #5, #11, and #16 show a high-level concentration. Station #16 is a roadside station, which is strongly affected by mobile vehicles. In order to examine the  
Figure 1: PM\({}_{2.5}\) (particulate matter of diameter less than 2.5 \(\upmu\)m) seasonal average concentrations are plotted for 18 monitoring stations across seasons for the period from 1 January 2015 to 31 December 2017. Stations #13, #15, and #18 show a relatively low level in concentration, while stations #5, #10, #11, and #16 show a high level in concentration.  
correlation structure of PM\({}_{2.5}\) concentrations obtained from spatially separated monitoring stations, the authors applied the DFA and the MFDFA methods to two groups, namely, G1 (stations #15 and #18) and G2 (stations #5, #11, and #16), consisting of time series with different characteristic seasonal statistics, as shown in Figure 2, among five PM\({}_{2.5}\) monitoring stations with representative statistics.  
In Figure 3, a seasonal trend is even clearer in G2 while a less clear one can be seen in G1.