Financial Risk Manager Part 1

Explanation

The Schwarz Information Criterion (SIC), also known as the Bayesian Information Criterion (BIC), provides the highest penalty factor based on degrees of freedom among the listed criteria.

Key Points:

• SIC/BIC has a penalty term of k·ln(n), where k is the number of parameters and n is the sample size
• Akaike Information Criterion (AIC) has a penalty term of 2k
• Mean Squared Error (MSE) and Unbiased Mean Squared Error do not include explicit penalty terms for model complexity

Why SIC has the highest penalty:

• For sample sizes n > 7, ln(n) > 2, making SIC's penalty larger than AIC's
• SIC is more conservative and less prone to overfitting
• SIC tends to select simpler models compared to AIC
• This makes SIC particularly useful when concerned about data mining and overfitting

Mathematical Comparison:

• AIC: -2ln(L) + 2k
• SIC/BIC: -2ln(L) + k·ln(n)
• Since ln(n) grows with sample size, SIC imposes a stronger penalty for additional parameters

Therefore, when worried about overfitting, SIC is the preferred criterion due to its higher penalty for model complexity.