Forecasting foreign direct investment using optimized Hausdorff fractional multivariate grey Bernoulli model

Purpose This study aims to propose a novel multivariate forecasting model to estimate the future foreign direct investment (FDI) inflow in Brazil. Design/methodology/approach This research introduces a novel forecasting model called the Hausdorff fractional NBGMC(p,n). This model is an extension of the original nonlinear grey Bernoulli model with convolution integral, known as NBGMC(1,n). The key innovation in this new model is the incorporation of the Hausdorff fractional accumulation operator, which provides greater flexibility in capturing complex data patterns, making it more effective to forecast FDI. The model boosts prediction accuracy, addressing one of the biggest challenges in FDI forecasting research. An added advantage of this approach is its simplification of computations. The model uses the recurrence relation of the binomial in the discrete solution, eliminating the need for Gamma function calculations – an issue that can complicate models with fractional orders. To further enhance the model’s performance, the Jaya algorithm is used to optimize its parameters. This algorithm is particularly useful due to its ability to fine-tune the model to adapt to different data sets, which helps deliver more accurate and reliable forecasts. Findings The proposed model’s effectiveness is tested with a case study on forecasting FDI from Brazil. The results reveal that the Hausdorff fractional NBGMC(p,n) model significantly outperforms traditional forecasting models in terms of both accuracy and predictive power. This shows its potential as a valuable tool for policymakers and investors who need more dependable methods to predict FDI trends in today’s global economy. Furthermore, the proposed model is used to predict the future FDI inflow in Brazil. Originality/value This study makes significant contributions by introducing a Hausdorff fractional model, integrated with a multivariate grey Bernoulli forecasting approach, which reduces computational complexity. In addition, the incorporation of the Jaya algorithm for variable optimization enhances both the model’s efficiency and accuracy. This novel framework is applied to forecast Brazil’s FDI inflow, offering valuable insights based on specific input variables. This approach not only advances predictive accuracy but also provides a novel perspective for economic forecasting in emerging markets. Furthermore, the proposed model is presented in a structured and practical manner, emphasizing the real-world applications. By highlighting key benefits, this research bridges the gap between advanced quantitative methods and decision-making needs in economic policy and investment strategies. By applying this framework to Brazil’s FDI forecasting, the study offers valuable insights for economic forecasting in emerging markets.