When running varselect in R, I usually get a few different models to choose from based on different statistics. I know of:

  1. Akaike information criterion (AIC)
  2. Bayesian information criterion (BIC) or Schwarz criterion (SC)
  3. Final Prediction Error (FPE) criterion
  4. Hannan–Quinn information criterion (HQC)

What is the practical difference between these tests and under what circumstances should I prefer one over the other?


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