Many studies have examined different fields of higher education expansion as well as the understanding of expansion through the relationship between higher education and other academic fields. This study examined how the expansion of higher education impacts STEM (science, technology, engineering and mathematics) programs and differentiates in the trajectories of Taiwan. This study aims to explore the expansion phenomenon related to the enrollment in STEM in expanding higher education. We used

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... he classical ARIMA model to provide forecasts for the Ministry of Education (MOE) dataset. We then implemented ARIMAX (a multivariate autoregressive integrated moving average model) method to deal with the two concurrent series. The data source of this study, the time series data of student enrollment in the STEM programs and total student numbers (1950 to 2018), retrieved from MOE, Taiwan. We conducted the cross-correlation function to check the relationships between the series. We employed the ARIMAX methods to select the best fit model to predict student enrollment in STEM programs. The result revealed the selected ARIMAX(1,2,1) works well to establish the best fit model to predict enrollment in STEM programs. This finding provided implication to educational policy makers to implement the innovative STEM programs.