Multiresolution Diffusion Entropy Analysis of time series: an application to births to teenagers in Texas

TL;DR

This paper introduces a multiresolution diffusion entropy analysis method to assess the information content and residual memory in non-stationary time series, demonstrated on teenage birth counts in Texas across different groups.

Contribution

The paper presents a novel multiresolution diffusion entropy approach for analyzing non-stationary time series, applied to demographic data to reveal group-specific patterns and residual structures.

Findings

Identified distinct patterns in birth counts among racial/ethnic groups.

Detected residual memory indicating unaccounted factors in the data.

Showed differences between married and unmarried teens over time.

Abstract

The multiresolution diffusion entropy analysis is used to evaluate the stochastic information left in a time series after systematic removal of certain non-stationarities. This method allows us to establish whether the identified patterns are sufficient to capture all relevant information contained in a time series. If they do not, the method suggests the need for further interpretation to explain the residual memory in the signal. We apply the multiresolution diffusion entropy analysis to the daily count of births to teens in Texas from 1964 through 2000 because it is a typical example of a non-stationary time series, having an anomalous trend, an annual variation, as well as short time fluctuations. The analysis is repeated for the three main racial/ethnic groups in Texas (White, Hispanic and African American), as well as, to married and unmarried teens during the years from 1994 to 2000 and we study the differences that emerge among the groups.