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FRM Part I · FRM Exam Part I · Stationary Time Series

When comparing candidate ARMA models estimated on the same sample, which statement about information criteria is correct?

The AIC and BIC both combine goodness of fit with a penalty for extra parameters, and the model with the lowest value is preferred. BIC penalizes parameters more heavily than AIC for all but tiny samples, so it tends to select more parsimonious models.

  1. AThe AIC and BIC are both penalized-fit measures, and the model with the lowest value is preferredCorrect
  2. BBIC imposes a smaller penalty per parameter than AIC for samples larger than 7 observations
  3. CThe model with the highest AIC is preferred because it has the greatest likelihood
  4. DInformation criteria can only be used to compare nested models

Explanation

AIC and BIC reward fit but penalize extra parameters, and lower values are preferred. BIC's penalty ln(T) per parameter exceeds AIC's penalty of 2 once T exceeds about 7, so BIC is the heavier penalty, not lighter. They can also compare non-nested models.

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