The conformable fractional grey system model.

Area of Science:

• Time Series Analysis
• Fractional Calculus
• Grey System Theory

Background:

• Fractional order grey models offer high effectiveness and flexibility in time series forecasting.
• Existing fractional order accumulation and difference methods are computationally complex, hindering theoretical analysis and practical application.

Purpose of the Study:

• To propose new definitions for fractional accumulation and difference based on conformable fractional derivatives.
• To develop a novel conformable fractional grey model for improved time series forecasting.
• To optimize the fractional order of the new model using the Brute Force method.

Main Methods:

• Introduction of conformable fractional accumulation and difference definitions.
• Development of a conformable fractional grey model.
• Optimization of the model's fractional order using the Brute Force method.
• Validation using numerical examples and benchmark datasets.

Main Results:

• The proposed conformable fractional grey model demonstrates feasibility and simplicity.
• The model outperforms existing fractional grey models and autoregressive models in short-term predictions (1-3 steps) across 21 benchmark datasets.
• The model shows superior performance in predicting natural gas consumption for 11 countries compared to existing fractional grey models.

Conclusions:

• The conformable fractional grey model offers enhanced efficiency for longer-term predictions.
• The model is particularly effective for forecasting non-smooth time series.
• The proposed methods simplify theoretical analysis and application of fractional grey models.