Statistical Analysis of the Impact of COVID-19 on PM_2.5 Concentrations in Downtown Quito during the Lockdowns in 2020

In this paper, a comparative analysis between the PM2.5 concentration in downtown Quito, Ecuador, during the COVID-19 pandemic in 2020 and the previous five years (from 2015 to 2019) was carried out. Here, in order to fill in the missing data and achieve homogeneity, eight datasets were constructed, and 35 different estimates were used together with six interpolation methods to put in the estimated value of the missing data. Additionally, the quality of the estimations was verified by using the sum of squared residuals and the following correlation coefficients: Pearson's r, Kendall's τ, and Spearman's ρ. Next, feature vectors were constructed from the data under study using the wavelet transform, and the differences between feature vectors were studied by using principal component analysis and multidimensional scaling. Finally, a robust method to impute missing data in time series and characterize objects is presented. This method was used to support the hypothesis that there were significant differences between the PM2.5 concentration in downtown Quito in 2020 and 2015-2019.