varselect in R, I usually get a few different models to choose from based on different statistics. I know of:
- Akaike information criterion (AIC)
- Bayesian information criterion (BIC) or Schwarz criterion (SC)
- Final Prediction Error (FPE) criterion
- Hannan–Quinn information criterion (HQC)
What is the practical difference between these tests and under what circumstances should I prefer one over the other?
Monte Carlo evidence suggests that the BIC penalty function works well in designs calibrated to macroeconomic data (Stock and Watson, 2011). It is common to run them all for comparison purposes.