A Hybrid Wavelet Analysis-Based New Information Priority Nonhomogeneous Discrete Grey Model with SCA Optimization for Language Service Demand Forecasting

Accurate forecasting of language service demand is essential for language industry planning and resource allocation, yet it remains challenging due to small sample sizes, noisy data, and nonlinear dynamics in industry-level time series. To enhance forecasting accuracy, this study proposes a novel hybrid forecasting framework, called the Sine Cosine Algorithm-optimized wavelet analysis-based new information priority nonhomogeneous discrete grey model (SCA–WA–NIPNDGM). By integrating wavelet-based denoising with the NIPNDGM, the model effectively extracts intrinsic signals and prioritizes recent observations to capture short-term trends while addressing nonlinear parameter estimation via heuristic optimization. Empirical studies are conducted across three high-demand sectors in China from 2000 to 2024, including manufacturing; water conservancy, environmental, and public facilities management; and wholesale and retail. The findings show that the proposed model displays superior performance to 11 benchmark grey models and five optimization algorithms across six evaluation metrics, achieving test Mean Absolute Percentage Error (MAPE) values as low as 1.2%, with strong generalization, stable iterations, and fast convergence. These results underscore its effectiveness in forecasting complex time series and offer valuable insights for language service market planning under emerging AI-driven disruptions.