COMPLEXITY, MULTIRESOLUTION, NON-STATIONARITY AND ENTROPIC SCALING: TEEN BIRTH THERMODYNAMICS

Abstract

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.

Keywords:

• Fractals
• Time Series
• Wavelet
• Teenagers
• Births

Notes

The first column reports the values of the entropy at the first step of diffusion, S(1), for the original data and their rests R_j for j = 2,…, 8. The second and third columns report the relative and the absolute values of the range of the height of the horizontal lines that measure the information or entropy that corresponds to each wavelet scale. The absolute values of the entropy of the third column are obtained by summing the values of column 1 and 2. The last column reports the main periodicity present in each rest R_j . The rests R ₈ and R ₇ are dominated by the annual periodicity and its harmonic. The rests R ₅, R ₄, R ₃ are dominated by the strong weekly periodicity. The values are compatible with those given by the spectral analysis of Figure 2.