## 1 Introduction  
Currently, most countries are facing severe air pollution problems incurred by rapid industrialization, high population density, traffic density, and so on. Air pollution levels are determined by the concentrations of the six pollutants, i.e., atmospheric fine particulate matters (PM\({}_{2.5}\) of diameter less than 2.5 \(\upmu\)m), atmospheric particulate matter (PM\({}_{10}\) of diameter less than 10 \(\upmu\)m), SO\({}_{2}\), NO\({}_{2}\), CO, and O\({}_{3}\). In particular, PM\({}_{2.5}\) is a critical pollutant linked to respiratory and cardiovascular diseases, as well as visibility degradation and climate change [1]. So far, there were many studies on the characteristics of PM\({}_{2.5}\) using three approaches: finding sources of emission and characterizing seasonal distributions [2; 3; 4; 5], analyzing various correlation structures inherent in PM\({}_{2.5}\) time series [6; 7; 8; 9], and developing theoretical models for prediction and control [10; 11; 12]. Most developing countries such as China and India are facing a severe air pollution problem. They feature a high concentration of PM\({}_{2.5}\), which is a direct effect of industrialization and urbanization. The concentration exhibits a seasonal trend, which is presumably due to the meteorological conditions [13]. However, there is no clear causal relationship between the PM\({}_{2.5}\) concentration and meteorological factors [7; 14], as only the evidence of cross-correlation can be detected. Since various DFA (detrended fluctuation analysis) approaches were used for correlation structures, many researchers reported various characteristics of complex correlation structures inherent in air pollutants [6; 7; 8; 9; 15; 16] after the advent of the method [17]. However, the effect of non-stationarities and trends on various scaling exponents was disregarded in the process of quantifying the degree of correlation. Since the seasonality is a noticeable phenomenon in air pollutant series, they may be misunderstood as spurious scaling indexes and crossover behavior if the authors do not consider these effects [18; 19; 20; 21]. Thus, the first goal of this paper was to properly interpret the characteristics of scaling functions of DFA, MEDFA (multifractal detrended fluctuation analysis), and DCCA (detrended cross-correlation analysis), and to present genuine correlation scaling exponents. Furthermore, the authors performed simulation analyses using the ARFIMA (auto-regressive fractionally integrated moving average) process with periodic trends by varying the degree of amplitude in order to understand the effect of seasonal trends. Lastly, there were attempts to develop a theoretic model to exhibit some facets of characteristics of air pollutant time series which failed to catch all empirical facts. In fact, empirical studies are very important to understand air pollution systems. We can establish a reliable framework on the basis of firm empirical facts when taking measures against spreading air pollutants. In this work, our aim was to discover heterogeneity in the dynamics underlying the PM\({}_{2.5}\) accumulation process in the Korean peninsula. To this end, we firstly explored the statistics of all available PM\({}_{2.5}\) datasets and generated two distinct groups with mass concentration levels. Then, we examined the auto- and cross-correlation structures of both groups using DFA-based methodologies. The Korean peninsula is located close to China, a country that is developing very rapidly. It is a well-known fact that the Korean peninsula is strongly affected by the inflow of air pollutants from China, although quantification of the effect remains controversial [22]. In fact, the events are intermittent in some respects, and they show seasonal trends in other respects, because, in the winter, coal-fuel combustion and heating increases, and, in the spring, dust occurs almost periodically.