The Improved Conformable Fractional Grey Model Using ADMM and HOA Algorithm

The grey model (GM) is a forecasting model known for its ability to provide accurate predictions for small sample data, but it struggles with complex nonlinear time series. This paper introduces a fractional calculus prediction model, utilizing Conformable Fractional Difference (CFD) and Conformable Fractional Accumulation (CFA) to calculate the new time series. The traditional least squares method for parameter estimation is transformed into a Least Absolute Shrinkage and Selection Operator (LASSO) problem and is solved using the dual form of the Alternating Direction Method of Multipliers (ADMM). Additionally, the Hiking Optimization Algorithm (HOA) is employed to optimize the fractional order parameter. As a result, the improved model demonstrates greater accuracy than the original model when dealing with small sample data.