Nonlinear Granger Causality using Kernel Ridge Regression
Wojciech "Victor" Fulmyk
I introduce a novel algorithm and accompanying Python library, named
mlcausality, designed for the identification of nonlinear Granger causal
relationships. This novel algorithm uses a flexible plug-in architecture that
enables researchers to employ any nonlinear regressor as the base prediction
model. Subsequently, I conduct a comprehensive performance analysis of
mlcausality when the prediction regressor is the kernel ridge regressor with
the radial basis function kernel. The results demonstrate that mlcausality
employing kernel ridge regression achieves competitive AUC scores across a
diverse set of simulated data. Furthermore, mlcausality with kernel ridge
regression yields more finely calibrated $p$-values in comparison to rival
algorithms. This enhancement enables mlcausality to attain superior accuracy
scores when using intuitive $p$-value-based thresholding criteria. Finally,
mlcausality with the kernel ridge regression exhibits significantly reduced
computation times compared to existing nonlinear Granger causality algorithms.
In fact, in numerous instances, this innovative approach achieves superior
solutions within computational timeframes that are an order of magnitude
shorter than those required by competing algorithms.