Gradient radial basis function networks for nonlinear and nonstationary time series prediction

Area of Science:

• Artificial Intelligence
• Time Series Analysis
• Machine Learning

Background:

• Radial basis function (RBF) networks are sensitive to nonstationary time series data, limiting their predictive accuracy.
• Traditional RBF networks struggle with time series exhibiting varying levels and trends.
• Nonstationary time series present challenges in accurate forecasting and pattern recognition.

Purpose of the Study:

• To develop a modified radial basis function (RBF) network capable of handling nonstationary time series with homogeneous nonstationary behavior.
• To enhance the predictive performance of RBF networks for chaotic time series.
• To introduce the gradient RBF (GRBF) model as an improvement over classical RBF networks.

Main Methods:

• Modified the structure of the RBF network's hidden nodes to detect and react to the gradient of the time series.
• Developed the gradient RBF (GRBF) model.
• Evaluated the single and multistep predictive performance using the Mackey-Glass chaotic time series.

Main Results:

• The GRBF model demonstrated superior predictive performance compared to the classical RBF model.
• Simulation results confirmed the effectiveness of the GRBF predictor for time series with and without a time-varying mean.
• The modified hidden node function effectively addressed the sensitivity issues of the original RBF network.

Conclusions:

• The gradient RBF (GRBF) model offers a significant improvement for predicting nonstationary time series.
• The GRBF model provides more robust and accurate forecasting, especially for chaotic series.
• The proposed modification effectively enhances the RBF network's ability to handle time series with homogeneous nonstationary behavior.