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IDK why this got downvoted, it's good to know there's a non-linear alternative to ARIMA. Here's J Lizier's implementation; it's in Java, but apparently usable in Python via Jpype.
For (what I understand to as) a mutual information analogue of correlation coefficients, there's a native Python implementation, ennemi.
In Python you can use the https://nixtla.github.io/mlforecast library for example, it makes the feature engineering, evaluation and cross validation trivial.