A wavelet analysis to compare environmental time series

Abstract

Cities such as São Paulo , Tokyo , New York and Mexico City are on the list of the most polluted in the world. PM10 is a major component of air pollution that threatens both our health and our environment. In this paper, we are interested in comparing time series using wavelet analysis. The comparison is made using three statistical procedures, namely, the scalogram, the test given by the ratio of cumulative wavelet periodograms and the analysis of variance. These methods are applied to compare the rates of hourly PM10 in four different districts of the city of São Paulo , Brazil . For the analysis we use the discrete wavelet transformation (DWT) considering the Haar and Daubechies wavelets. In the analysis of variance for the wavelet coefficients, we tested the local effect considering the months from June to October as replications. Scalograms were constructed for each series and we note that for the two wavelet bases used they presented different behavior leading to the conclusion that the series of energies are different. The effect of location was significant in the analysis of variance considering levels for both bases Haar and Daubechies DWT. We also consider a statistical test at each level j given by the ratio of the cumulative wavelet periodograms of the series. Again we could find that the series are generated by different processes.