Optimized Nonlinear Grey Bernoulli Model for Nowcasting the Philippine Gross Domestic Product

Abstract

This study advances an optimized Nonlinear Grey Bernoulli Model (NGBM(1,1)) for nowcasting the gross domestic product of the Philippines. Two parameter optimization strategies, Particle Swarm Optimization (PSO) and the use of an exponential background value, were employed to minimize out-of-sample mean absolute percentage error. A harmonic function simulation identified a 70/30 training-to-testing ratio as the most effective data-splitting scheme. Applied to quarterly GDP data from the first quarter of 2021 to the fourth quarter of 2024, the PSO-optimized NGBM(1,1) yielded the lowest out-of-sample mean absolute percentage error of 5.45 percent and the lowest root mean square error, outperforming benchmark models. Results indicate that PSO provides substantial improvements in NGBM(1,1) forecasting performance, whereas the exponential background method yields comparatively smaller gains.