Estimating HURST exponent and fractal dimension UV-VIS absorbance time series analysis

Abstract

The objective of this study is to estimate the exponent or Hurst parameter and the fractal dimension for UV-Vis spectrometry time series analysis, using principal component analysis (PCA). This analysis is performed to understand if the UV-Vis absorbance time series are persistent, anti-persistent, deterministic or white noise.  Three different UV-Vis absorbance time series for three different study sites were used: (i) Salitre wastewater treatment plant (WWTP) in Bogotá; (ii) Gibraltar pumping station (GPS) in Bogotá; and (iii) San Fernando WWTP in Itagüí (south of Medellín). Each of these time series had an equal number of samples (5705). The dimensionality of the absorbance spectra, given their high correlation, was reduced using PCA and the first principal component was used for each study site. For the three study sites, this first principal component explained from 82% to 94% of the variability. The Hurst exponents were determined: (i) 0.8 for Salitre WWTP; (ii) 0.85 for GPS; and (iii) 0.89 for San Fernando WWTP. Using Hurst exponent values, for the three UV-Vis absorbance time series at same study sites, fractal dimensions were determined and a fractal dimension average of 1,153 was obtained. The three UV-Vis absorbance time series are persistent and have high self-similarity since the Hurst exponent is greater than 0.5.