An Optimization Scheme for Enhancing the Performance of Fractional-order Grey Prediction Models in Seasonal Forecasting Tasks: the Case of the Fractional-order GM(1,1) Model

Fractional-order grey prediction models have gained wide recognition for their computational efficiency and straightforward modeling mechanisms. However, their performance in seasonal forecasting tasks still needs improvement. To address fress this, this paper designs a novel optimization scheme and applies it to the representative fractional-order grey GM(1,1) model (FGM(r,1)) to advance research in this area. In this optimization scheme, the dummy variable is used to enable the model to directly handle seasonal time series, the discretization technique is employed to simplify the computational steps, and the Bernoulli parameter and the linearly weighted hybrid fractional-order accumulation strategy are used to enhance the model's fitting capability. To verify the effectiveness of the proposed method, the optimized model and some benchmark algorithms are used to model three quarterly data sets. The experimental results show that the optimized model can produce better performance, which verifies the effectiveness of this optimization scheme.