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

TL;DR

This paper introduces a combined wavelet and entropy-based methodology to analyze complex, non-stationary teen birth data, effectively separating deterministic trends from stochastic components across multiple scales.

Contribution

It develops a novel approach integrating wavelet multiresolution analysis with Diffusion Entropy Analysis to study non-stationary time series in demographic data.

Findings

Successful separation of deterministic and stochastic components in teen birth data

Identification of scale-dependent stochastic information in birth rates

Effective smoothing and analysis of long-term demographic trends

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 {\it scale-by-scale} manner. The {\it scale-by-scale} decomposition generates smooth and detail curves which 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 upon 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 to teens in Texas during the period from 1964 to 1999.