###### Abstract
First, we took the decision to study only one of the particulates, precisely PM\({}_{2.5}\)--because it is well known that PM\({}_{2.5}\) is one of the air pollutants with a more positive correlation with the virus spread, as witnessed by many recent studies [24]. With regard to this important point, we can anticipate that the average values of that pollutant, measured in micrograms/m\({}^{3}\) in NYC during the first epidemic outbreak (February-March 2020), were from 20% to 25% higher than the average values computed for a longer period that extends from February to July 2020. Second, we decided to analyze the pollution/infections data relative to two different types of counties, belonging to the state of New York. Obviously, we were particularly interested in studying the situation of the metropolitan area of NYC, with its five counties which coincide with the renowned boroughs, namely: New York (Manhattan), Kings (Brooklyn), Bronx (The Bronx), Richmond (Staten Island), and Queens (Queens). Nonetheless, in addition to these, we also studied some other neighboring counties, including: Nassau, Suffolk, Rockland, and Westchester. Moreover, to evaluate whether the association we were trying to validate was only valid for urban, densely populated areas, very close to the city, such as those we have just mentioned, we decided to extend our analysis also to other, more peripheral counties, including: Onondaga, Oneida, and Monroe. This way, we have been able to test two different situations: Both densely populated and less-populated areas, with their different relative values, in terms of COVID-19 infections and amount of pollution. Third, and finally, we examined two different time series in the period of interest (February-March 2020): The number of daily infections vs. the registered values of PM\({}_{2.5}\) circulating in the air, daily. The daily COVID-19 infections data was provided by the New York State Department of Health, while the registered values of PM\({}_{2.5}\) come from the United States Environmental Protection Agency. To check whether an association could be established between these two series of data, we adopted two different methodologies: Granger causality and machine learning. We first subjected those temporal series of data to a Granger causality statistical hypothesis test. Testing for Granger causality means verifying the statistical hypothesis that a time series \(X\) Granger-causes another time series \(Y\): In other words, \(X\) values would better predict the future values of \(Y\), beyond the information contained in past values of \(Y\) alone. To do that, two different regression models are, typically, tested on the \(Y\) values. The first one uses only previous values of \(Y\), while the second exploits both previous \(Y\) values, plus lagged values of \(X\). If those tests are successful, it can be concluded that values provide statistically significant predictive information about future values of \(Y\). In simple words, \(X\) Granger-causes \(Y\). Unfortunately, many believe that the use of Granger causality tests can be questionable, if one aims at demonstrating a clear cause-effect correlation. Nonetheless, we argue that, with two different types of counties of the state of New York under investigation (that is, densely populated and less-populated areas), the results of this study have shown that an association between the two time series can be confirmed, well beyond the limit of a weak interpretation of causality, as 33 over 36 statistical tests have confirmed the hypothesis, with a \(p\)-value less than 0.05. Then, to provide further evidence in favor of this correlation, we conducted a second, additional series of experiments, using machine learning (ML) algorithms. Specifically, four different ML algorithms were used in the following (non-traditional) way.