In this study, we present a novel constraint-based algorithm for causal structure learning specifically designed for nonlinear autoregressive time series. Our algorithm significantly reduces computational complexity compared to existing methods, making it more efficient and scalable to larger problems. We rigorously evaluate its performance on synthetic datasets, demonstrating that our algorithm not only outperforms current techniques, but also excels in scenarios with limited data availability. These results highlight its potential for practical applications in fields requiring efficient and accurate causal inference from nonlinear time series data.

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