Time series modeling of secondary school enrollment in Ecuador: a Box–Jenkins analysis (1971–2023) - Haymacaña Moreno, Edwin; Zapata Aspiazu, Leonor Alejandrina; Duque-Aldaz, Francisco Javier; Félix Genaro,; Sánchez Ancajima, Raúl Alfredo (Ingeniería Química y Desarrollo, 2026)
School enrollment analysis constituted a key indicator to evaluate coverage and equity in national education systems. The objective of this study was to model secondary school enrollment in Ecuador during 1971–2023 using time series techniques. Official national and international data were employed to construct an annual net enrollment series. The methodological procedure included descriptive analysis, stationarity tests (ADF and KPSS), first-order differencing, identification and estimation of candidate models through the Box–Jenkins approach, optimal selection with auto.arima, residual validation via Ljung–Box tests, out-of-sample error metrics (MAE, RMSE, MAPE), and forecasts for 5–10 years. All processing was performed in R Studio with specialized time series modeling packages. The results showed that after first-order differencing, the series achieved stationarity. The selected model adequately explained enrollment dynamics, with residuals consistent with white noise and without significant autocorrelations. Validation metrics indicated good predictive accuracy, with low mean absolute and percentage errors. Projections suggested a moderate and sustained growth trend in enrollment, though with signs of stabilization in the longer horizon. This study demonstrated the usefulness of Box–Jenkins models for analyzing educational phenomena, providing quantitative evidence for public policy formulation and recommending the expansion of more complete historical datasets in future research.
Keywords: Time Series; ARIMA; Box–Jenkins; School Enrollment; Secondary Education; Ecuador; Educational Forecasting