## 5 Conclusions  
This study identified an appropriate time-series methodology to estimate the supply of the S&T workforce. To account for the data's limitations, we selected exponential smoothing methods and the Prophet model, and used South Korea as a case study to validate the methods. Our forecasts for the S&T doctorate supply for a period of 20 years, from 2021 to 2040, clarified that the Prophet model outperforms traditional methods such as exponential smoothing in workforce supply predictions. Therefore, the Prophet model can serve as a benchmark for future forecasting models focusing on the supply of S&T human resources in Korea. Similarly, our findings indicate that the Prophet model may be effectively applied to workforce forecasting studies in other countries and sectors, despite having potential variations across disciplines and regions. Furthermore, this study indicates that, compared to traditional time-series models, state-of-the-art models like Prophet provide better predictive performance regarding estimating S&T workforce trends.  
Our findings predict medium- to long-term workforce supply trends for S&T PhD scholars in South Korea. Earlier studies anticipated an increase in demand for PhD scholars in various industries, including S&T. Although the demand for S&T PhD scholars specializing in R&D planning, evaluation, and policy formulation is growing, the scholars' roles will not be confined to these areas alone. The S&T doctoral workforce in South Korea is projected to grow at a rate that is consistent with current trends until 2028; subsequently, it will decline and eventually recover after 2035. During this 7-year period, targeted policy measures are needed to support the rising number of doctoral scholars and ensure an upward trend after 2035. Since the global landscape is evolving and technological hegemony is on the rise, it is imperative to foster a robust pipeline of core S&T talent. As previously noted, human resource development is a multifaceted challenge that cannot be addressed by a single policy. A comprehensive and dynamic policy framework, incorporating various initiatives in collaboration with relevant government departments, is essential to bolster national competitiveness. Such efforts must be sustained to ensure evidence-based policy implementation.  
Further, we plan to continue refining this forecasting model to ensure its broad applicability in supporting policies while overcoming various constraints. Many of the earlier studies on time-series forecasting suggest combining different types of prediction models. However, owing to data limitations, we could apply only a limited number of models in this study. Therefore, future research will utilize additional time-series data and models such as LSTM and ARIMA to conduct more robust comparative analyses. If these models are found to improve performance, ensemble models combining various configurations can be proposed. Once additional data become available, multivariate time-series models such as the vector error correction model can be explored as well. These future research ideas can be realized only if longer time-series data become available. This study benchmarks existing forecasting models, and future research should prioritize the exploration of novel methodologies. Applying these approaches across countries and sectors will enable comprehensive comparisons of global supply trends to obtain deep insights. This is crucial to the advancement of the field of policy science.  
Conceptualization, H.-Y.Y. and H.C.; Methodology, H.-Y.Y.; Writing--original draft, H.-Y.Y.; Writing--review & editing, H.-Y.Y. and H.C.; Supervision, H.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
All data generated or analyzed during this study are included in this published article.  
All authors would like to thank the reviewers for their valuable contributions that have enhanced the quality of our research. The authors declare no competing interests.