Non-extensive diffusion entropy analysis: non-stationarity in teen birth phenomena

TL;DR

This paper introduces a non-extensive Tsallis q-entropy approach to analyze non-stationarity in time series, applied to teen birth data, revealing social influences with memory effects.

Contribution

It extends diffusion entropy analysis with Tsallis q-entropy to quantify non-stationarity, applied here to social data on teen births.

Findings

Unmarried teen births show stronger social memory effects.

Non-stationarity is more pronounced in unmarried teen birth data.

Wavelet analysis helps interpret social influences on birth trends.

Abstract

A complex process is often a balance between non-stationary and stationary components. We show how the non-extensive Tsallis q-entropy indicator may be interpreted as a measure of non-stationarity in time series. This is done by applying the non-extensive entropy formalism to the Diffusion Entropy Analysis (DEA). We apply the analysis to the study of the teen birth phenomenon. We find that the unmarried teen births are strongly influenced by social processes with memory. This memory is related to the strength of the non-stationary component of the signal and is more intense than that in the married teen time series. By using the wavelet multiresolution analysis we attempt to give a social interpretation of this effect.