Nonlinear Processes in Time-Ordered Observations: Self-­Organized Criticality in Daily High School Attendance

Abstract

In the United States, high school attendance and drop-°©‐‑out are important policy concerns receiving extensive coverage in the research literature. Traditionally, the focus in this work is on the summary of dropout rates and mean attendance rates in specific schools, regions or socio-economic groups. However, the question how stable those attendance rates are over time has received scant attention. Since instability in attendance may affect how long individual students stay in school, the issue deserves attention. Theschool districts that have begun to keep record of daily attendance rates in their schools over multi-year periods, such as those in New York City, have created an opportunity to investigate the temporal dimension of daily attendance, and thereby explore its stability. This paper will focus on its long-term characteristics, specifically the following: self-similarity, meta-stability or pink noise, and the impact of sudden departures from the central tendency of the series. Such departures can be used to estimate the impact of exogenous influences on the behavior of the system. The findings illustrate the importance of describing the dynamical patterns underlying attendance that remain concealed in traditional summary measures.