Estimating Perturbation and Meta-Stability in the Daily Attendance Rates of Six Small High Schools

Abstract

This paper discusses the daily attendance rates in six small high schools over a ten-year period and evaluates how stable those rates are. “Stability” is approached from two vantage points: pulse models are fitted to estimate the impact of sudden perturbations and their reverberation through the series, and Autoregressive Fractionally Integrated Moving Average (ARFIMA) techniques are used to detect dependencies over the long range of the series. The analyses are meant to (1) exemplify the utility of time series approaches in educational research, which lacks a time series tradition, (2) discuss some time series features that seem to be particular to daily attendance rate trajectories such as the distinct downward pull coming from extreme observations, and (3) present an analytical approach to handle the important yet distinct patterns of variability that can be found in these data. The analysis also illustrates why the assumption of stability that underlies the habitual reporting of weekly, monthly and yearly averages in the educational literature is questionable, as it reveals dynamical processes (perturbation, meta-stability) that remain hidden in such summaries.