Granger causality test with nonlinear neural-network-based methods: Python package and simulation study.

Area of Science:

• Neuroscience
• Economics
• Data Science

Background:

• Granger causality (1969) is a foundational concept in time-series analysis.
• Increasing interest in nonlinear causality necessitates advanced analytical tools.
• Existing methods may not capture complex, nonlinear dependencies between signals.

Purpose of the Study:

• To present a novel nonlinear causality analysis method using neural networks.
• To introduce a user-friendly Python package for implementing this method.
• To demonstrate the package's capability in detecting nonlinear causal relationships.

Main Methods:

• Utilized Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Multilayer Perceptron (MLP) neural networks.
• Tested on simulated signals with and without nonlinear dependencies.
• Employed a 70/30 train-test split and Wilcoxon signed-rank test for error comparison.

Main Results:

• Neural network models successfully detected nonlinear causality where traditional autoregressive (AR) models failed.
• Multilayer Perceptron (MLP) achieved superior prediction accuracy (MSE=0.011).
• Proposed models demonstrated high reliability, avoiding false causality detection.

Conclusions:

• The neural-network-based approach effectively detects nonlinear causality missed by classical Granger methods.
• The developed Python package offers a robust tool for analyzing causal relationships and their temporal dynamics.
• This method provides accurate forecasting and reliable causality detection, outperforming existing techniques.