Modeling of measurements on the basis of non-linear transformations of time series

This paper presents a time series analysis of PM<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</inf> concentration measurements in downtown Quito, Ecuador, during 2015-2021. The objective is to develop a forecasting model based on both past and current values of the measurements. Here, the dependence between adjacent observations is analyzed and 9 linear and nonlinear transformations of the time series are presented to eliminate trends and seasonal components. Then, an ARIMA model is obtained for the 2015–2019 data, and forecasts are made for 2019, 2020 and 2021 with the data from the years prior to each of these years. In addition, 95% confidence bands are calculated to express the accuracy of the forecast using probability limits. Next, the observations are classified by quarters and by being either inside or outside the confidence bands, and a comparative analysis is made between before the COVID-19 pandemic, the most difficult year of the pandemic, 2020, and the year when we were already overcoming the pandemic, 2021. Finally, the results show that the proposed model captured most of the variability of the series, and brought out the changes in PM<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</inf> concentration produced by lockdowns and restrictions on circulation in the city due to SARS-CoV-2.