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

Two models are fitted to the same 100 observations. Model A (AR(1)) has 2 estimated parameters and a residual sum of squares of 80. Model B (AR(3)) has 4 estimated parameters and a residual sum of squares of 72. Using the criterion AIC = ln(RSS/T) + 2k/T, which statement is correct?

AIC prefers Model B. Model A scores about -0.183 and Model B about -0.249, and the lower value wins. The reduction in residual variance from B outweighs the added penalty for two extra parameters.

  1. AAIC prefers Model A because its penalty term is smaller and the fit improvement in B is outweighed
  2. BAIC prefers Model B because ln(72/100) is lower and the improvement exceeds the extra penaltyCorrect
  3. CAIC cannot compare models with different numbers of parameters
  4. DThe two models have identical AIC values

Explanation

A: ln(0.80) = -0.2231, plus 4/100 = 0.04, giving -0.1831. B: ln(0.72) = -0.3285, plus 8/100 = 0.08, giving -0.2485. B has the lower AIC, so B is preferred. The extra penalty of 0.04 is smaller than the fit gain of 0.105.

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