Forecasting University Enrolment Amid Crisis and Admission Restructuring: A Phase-Aware Regression Model For A 15-Year Series (2011–2025)

Abstract

Enrolment forecasting is a core input to planning teaching staff, classrooms, laboratories, dormitories and budgets. Institutional series, however, are short and may contain regime changes caused by external shocks or by reforms of admission policy. This study uses a 15-year enrolment series (2011–2025) from Thu Dau Mot University, Ho Chi Minh City, Vietnam, to test for structural breaks and to develop a Phase-Aware Weighted Least Squares (PA-WLS) model. The specification combines a time index rebased at 2011 with two phase indicators — the COVID-19 period (2020–2022) and the admission restructuring period (2023–2024) — and downweights the volatile observations from 2020–2024.

The Chow test identifies a significant break at 2023 (F = 7.098, p = 0.011), and the joint test of the phase effects is also significant (F = 5.328, p = 0.024). PA-WLS estimates a baseline trend of 175.72 students per year, a level shift of +1,903.26 for the pandemic phase, and a level shift of −1,979.21 for the restructuring phase. Across eight rolling origins, the MAPE is 16.22%, compared with 27.28% for a linear trend over time. With only eight origins, this 11.06-point gap does not reach significance at the 5% level (paired t = −1.437, p = 0.194; Diebold–Mariano DM = −1.707, p = 0.132). None of the four nonlinear machine-learning algorithms outperforms the phase-aware specifications under the same protocol; the tree ensembles achieve a near-perfect in-sample fit yet forecast the worst out of sample.

Re-estimation on the full series yields point forecasts of 6,390 students for 2026 and 6,566 for 2027, with 95% prediction intervals of [4,274; 8,506] and [4,368; 8,763]. Sensitivity analysis shows that the choice of specification shifts the 2026 forecast by 6,001–6,861 students, roughly 37 times the range induced by the weighting parameter. The practical value of the procedure lies less in a single point estimate than in identifying regime change, validating out-of-sample, and quantifying uncertainty for scenario-based planning.