Forecasting primary healthcare resources in China using a grey convolutional multivariate self-memory combination model GMC-SM(1,n)

Purpose China is entering a moderately aging society, in which the demand for primary healthcare resources is characterized by small samples, multiple influencing factors and strong temporal dependence. This study proposes a novel grey forecasting approach to improve prediction accuracy and stability for primary healthcare resource demand under incomplete information. Design/methodology/approach Drawing on empirical data for primary healthcare institutions and beds in China, this study employs grey relational analysis to identify key driving variables and develops a grey convolutional multivariate self-memory combination model, denoted as GMC-SM(1,n), by integrating grey system theory with the self-memory principle and compares it with classical grey prediction models. Findings The proposed GMC-SM(1,n) model exhibits superior accuracy, with fitting and prediction MAPEs of 1.02% and 0.28% for institutions, and 1.93% and 0.82% for beds. The model also achieves lower root mean square error, mean absolute error and standard deviation of errors (SD) than comparative models, demonstrating strong robustness and an enhanced ability to capture multivariable coupling and temporal dependence with small samples. Practical implications The results reliably support dynamic resource allocation and long-term planning under population aging, offering practical reference value for policymakers. Originality/value This study enriches grey forecasting methodology by integrating a self-memory mechanism into the grey convolutional multivariate framework, effectively addressing the issues of historical dependence and initial value sensitivity inherent in traditional models.