Investigating the Long Memory Process in Daily High School Attendance Data

Abstract

While high school attendance is a well-known mediator in the relationship between educational attainment, background variables such as poverty and parental support on the one hand and instructional and school policy variables on the other, the study of high school attendance as a variable of interest in its own right is extremely rare in education. At most, it is reported in aggregated form without an estimation of its variability over time. The analysis presented in this chapter demonstrates how nonlinear time series analysis, autoregressive fractionally integrated moving average (ARFIMA) methods in particular, can be used to analyze high school daily attendance rates over a long time period (7 years) to obtain a fine-grained assessment of the time dependency of attendance behavior. The chapter first discusses through simulated examples how error dependencies can play out over a longer time spectrum (e.g., short-term autoregression, pink noise, Brownian motion), and then presents an analysis of real daily high school attendance data to illustrate these dependencies. The analyses show evidence of self-organized criticality (pink noise) in some but not all schools analyzed, a finding that indicates that attendance rates are more stable and predictable in some schools than in others.