Forecasting Real GDP Using a Multivariable Fractional Grey Model: An Empirical Application to Eastern European Countries

In recent years, the application of gray models for forecasting has gained significant attention in economic research. Grey system theory provides a robust methodology for analyzing and predicting time-series data characterized by uncertainty, limited information, and small sample sizes. This is particularly relevant for GDP forecasting, where macroeconomic data may be incomplete or noisy. This study introduces an optimized multivariable Hausdorff fractional gray Bernoulli forecasting approach to predict the real GDP using the variables in Cobb-Douglas production function. The proposed model’s effectiveness is tested with a case study on forecasting real GDP in five Eastern European transition economies: Bulgaria, Czech Republic, Hungary, Poland, and Romania. The empirical analysis reveals heterogeneous growth patterns: capital accumulation and significantly drives output in four countries. The proposed forecasting model achieves superior predictive accuracy significantly outperforms traditional forecasting models. Rolling window validation confirms the model’s robustness across varying forecast horizons. The projections indicate a steady, though moderating, growth trajectory across five countries through 2030. The methodology demonstrates its potential as a valuable tool for policymakers and economic planners who need more dependable methods to predict GDP trends in transition economies.