Financial Risk Manager Part 1

The Schwarz information criterion (SIC) is the most consistent selection criteria with the greatest penalty factor for degrees of freedom.

Explanation:

When selecting a linear trend model, different statistical measures have different properties:

1. S² - This is the sample variance, which is not typically used as a model selection criterion.

2. Schwarz information criterion (SIC) - Also known as Bayesian Information Criterion (BIC), this is the most consistent selection criteria. It has a stronger penalty for additional parameters than AIC, which makes it more likely to select the true model as sample size increases.

3. Akaike information criterion (AIC) - While widely used, AIC tends to select more complex models than SIC and is not consistent in the statistical sense (it doesn't necessarily select the true model as sample size goes to infinity).

4. Basic MSE - Mean Squared Error is a measure of model fit but doesn't penalize model complexity, so it tends to favor overfitted models.

The key advantage of SIC is its consistency property - as sample size increases, the probability of selecting the correct model approaches 1. This consistency comes from its penalty term, which grows with the sample size, making it more conservative than AIC.