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

A model is estimated over 200 observations. For a model with k = 4 parameters, the total sum of squared residuals is 150 and the AIC is defined as ln(SSR/T) + 2k/T. A competing model has k = 2 with SSR = 190. Using this AIC definition, which is correct? (ln(0.75)=-0.2877, ln(0.95)=-0.0513)

The four-parameter model is preferred with an AIC of about -0.2477, versus about -0.0313 for the two-parameter model. Each AIC equals the log of mean squared residual plus 2k/T, and the lower value wins. Ignoring the penalty would give -0.2877.

  1. AThe k = 2 model is preferred, AIC about -0.0413
  2. BThe k = 4 model is preferred, AIC about -0.2477Correct
  3. CThe two models have equal AIC
  4. DThe k = 4 model is preferred, AIC about -0.2877

Explanation

Model k=4: ln(150/200)=ln(0.75)=-0.2877; penalty 8/200=0.04; AIC=-0.2477. Model k=2: ln(0.95)=-0.0513; penalty 4/200=0.02; AIC=-0.0313. The k=4 model has the lower AIC. Option -0.2877 ignores the penalty.

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