A novel generalized nonlinear fractional grey Bernoulli model and its application

Considering that the existing fractional order grey prediction models are difficult to directly handle the shortcomings of seasonal time series, a novel generalized nonlinear fractional grey Bernoulli model capable of handling both seasonal and conventional time series is constructed. The structure of the new model adopts a more flexible nonlinear Bernoulli equation and a novel adaptive fractional accumulation operation, which endows it with stronger nonlinear fitting capabilities. Furthermore, the introduction of a dynamic parameter endows it with the capability to handle both seasonal and conventional time series simultaneously. Specifically, the structural parameters of the model are no longer obtained through traditional least squares method but instead through a moving average trend removal method and intelligent optimization algorithms, which greatly improves the computational efficiency of the model. Therefore, the practicality of the novel model surpasses that of all existing fractional grey prediction models. Experimental results on two types of datasets demonstrate that the proposed method outperforms existing machine learning models, fractional grey prediction models and statistical prediction model in terms of generalization ability, validating its effectiveness.