Calculation and realization of new method grey residual error correction model.

Area of Science:

• Time Series Analysis
• Mathematical Modeling
• Data Science

Background:

• Stochastic volatility series pose challenges for accurate prediction.
• Existing grey models (GM(1,1)) have limitations in prediction accuracy.
• Residual error analysis is crucial for model improvement.

Purpose of the Study:

• To improve the prediction accuracy of the grey model (GM(1,1)) for stochastic volatility series.
• To introduce a novel method for optimizing grey model predictions using residual errors.
• To develop and validate a wavelet residual-corrected grey prediction model (WGM).

Main Methods:

• Utilizing a new fitting method combining wavelet function basis and least squares to fit residual data.
• Constructing a residual prediction function based on the fitted residual data.
• Modifying the grey model (GM(1,1)) prediction function with the developed residual prediction function.
• Implementing the wavelet residual-corrected grey prediction model (WGM).

Main Results:

• The proposed wavelet residual-corrected grey prediction model (WGM) was successfully developed.
• Test results indicate that the WGM achieves significantly improved fitting accuracy compared to the standard GM(1,1).
• The WGM demonstrates irreplaceable advantages in fitting accuracy for stochastic volatility series.

Conclusions:

• The wavelet residual-corrected grey prediction model (WGM) effectively addresses the prediction accuracy limitations of the standard grey model (GM(1,1)).
• The novel approach of optimizing residual errors using wavelet functions offers a robust method for enhancing time series prediction.
• The WGM is a promising tool for accurate prediction of stochastic volatility series.