Bayesian Information Criterion (BIC)
Like AIC, but penalizes model complexity more heavily as the dataset grows, tending to pick simpler models.
The Bayesian Information Criterion is calculated the same way as AIC — goodness of fit minus a complexity penalty — but its penalty grows with the size of the dataset, so on a long history like this site's (2009-present) it usually favors a shorter lag length than AIC does.
This site reports both AIC and BIC across a range of candidate lag lengths on the diagnostics page, and highlights the length each one selects.