Complexity, multiresolution, non-stationarity and entropic scaling: Teen birth thermodynamics

This paper presents a statistical methodology for analyzing a complex phenomenon in which deterministic and scaling components are superimposed. Our approach is based on the wavelet multiresolution analysis combined with the scaling analysis of the entropy of a time series. The wavelet multiresolution analysis decomposes the signal in a scale-by-scale manner. The scale-by-scale decomposition generates smooth and detail curves that are evaluated and studied. A wavelet-based smoothing filtering is used to estimate the daily birth rate and conception rate during the year. The scaling analysis is based on the Diffusion Entropy Analysis (DEA). The joint use of the DEA and the wavelet multiresolution analysis allows: 1) the separation of the deterministic and, therefore, non-scaling component from the scaling component of the signal; 2) the determination of the stochastic information characterizing the teen birth phenomenon at each time scale. The daily data cover the number of births phenomenon at each time scale. The daily data cover the number of births to teens in Texas during the period 1964-1999.