A discrete nonlinear grey multivariate forecasting model and its application

Grey forecasting models have received increasing attention in recent years due to their suitability for small sample modeling. However, most existing approaches mainly focus on improving forecasting accuracy, while paying limited attention to how these improvements affect numerical stability. As a result, some developed models may not work reliably in certain scenarios. To support the development of stable and efficient grey forecasting methods, this paper constructs an effective discrete nonlinear grey multivariate forecasting model, referred to as EDNGMM. Specifically, EDNGMM introduces a concise and efficient fractional order accumulation operation, where the fractional order parameter enhances the flexibility of the modeling sequence. It also introduces a scaling parameter to adjust the magnitudes of different variables, which helps mitigate ill-conditioning in the coefficient matrix caused by scale differences and improves numerical stability. In addition, the model incorporates a Bernoulli nonlinearity parameter and a polynomial time trend term to strengthen nonlinear fitting and to describe the deterministic trend of the system over time. To select the hyperparameters of EDNGMM, we compare several population-based optimization algorithms and provide a simple selection procedure. Experiments on multiple data sets show that EDNGMM achieves competitive forecasting accuracy compared with baseline methods and demonstrates favorable stability.