TESTING FOR THE MULTIFRACTALITY IN AIR POLLUTANTS TIME SERIES AND APPLICATION TO TABUK REGION CASE STUDY

Fractal analysis of time series aims to extract the hidden or complex structures issued from the associated real data, such as scaling laws, non-stationary, dynamics, and so on. In this work, the air quality index and its components are considered as time series possessing fractal structures. The main objectives of the paper are, first, to confirm this fractality, and understand the underlying dynamics via a wavelet multifractal approach starting with a wavelet multifractal spectrum test to confirm the multifractality of the underlying data, and second, to propose a new model improving the classical min–max one, provided with a statistical measure for the adequacy of the new model. The theoretical findings are applied to the northwest Tabuk region of Saudi Arabia for environmental and climate data related to pollutants and factors involved in the estimation of the air quality index. The study showed that, effectively, the understanding of the hidden structure of the air pollution components, such as the fractality, helps in the exploration of suitable models to measure the associated indexes and their dependence. The study helped prove this fractality for both the concentrations and the dynamics of the pollutants. Developing a quantitative mathematical model based on these properties is of great interest for several purposes such as forecasting.