Alternative lag search strategies to complement exhaustive minimum p-value

[cbueth]

Currently find_optimal_lag evaluates all user-specified lags and returns the one with the best p-value. This is correct but can be costly for many lags. A few other approaches from the literature:

• Information criteria (AIC/BIC/HQ): standard VAR lag selection, could be offered alongside p-value minimization. statsmodels (https://www.statsmodels.org/stable/vector_ar.html#var-model), Wikipedia (https://en.wikipedia.org/wiki/Granger_causality)
• Sequential LR test: tests from largest to smallest lag, stopping when removing a lag significantly hurts fit. More conservative than AIC. Sylvester et al. 2026 (https://s2.smu.edu/~mitch/ftp_dir/pubs/sai26.pdf)
• Granger Minimum p-value (GMP): what we already do, but Sylvester et al. formalize it as a selection criterion vs AIC/BIC. Also Sylvester et al. 2026
• Regularization (group lasso / hierarchical lasso): automatically selects lags during VAR estimation by shrinking coefficients, avoids separate lag search. Nicholson et al. 2017 (https://pmc.ncbi.nlm.nih.gov/articles/PMC10571505), Time-varying Group Lasso (2022) (https://www.sciencedirect.com/science/article/pii/S0031320322002709)
• Neural GC with built-in lag selection: cMLP/cLSTM with hierarchical group lasso penalties learn both causality and lag order in one pass. Tank et al. 2021 (https://pmc.ncbi.nlm.nih.gov/articles/PMC10571505)

Adding an alternative strategy behind a lag_selection parameter would be a larger change, but would open up new usage groups.

If you are interested it, please react here or add a comment with suggestions.