Redo this problem using Akaike Information Criterion Corrected for bias (AICC).

Question

Redo this problem using Akaike Information Criterion Corrected for bias (AICC). Did your conclusions change?

The three models AR(2), MA(1), and ARMA(2, 1) are fitted to the following time series: The results using R are as follows: The models are ranked using Akaike Information Criterion (AIC): AIC = -2 times log-likelihood + 2 times number of free parameters. Determine the order from the best to worst model. Give full explanation on how you arrived to your answer. Show calculations. A. AR(2), MA(1), ARMA (2, 1) B. AR(2), ARMA (2, 1), MA(1) C. MA(1), AR(2), ARMA (2, 1) D. MA(1), ARMA (2, 1), AR(2) E. ARMA (2, 1), AR(2), MA(1).

Explanation / Answer

Since we always want to maximize the log likelihood the order from best to worst model is:

ARMA(2,1) > AR(2) > MA(1) i.e. E option

AIC of AR(2) = 76.8 (No. of free parameters = 2)

AIC of MA(1) = 75.02 ((No. of free parameters = 1)

AIC of ARMA(2,1) = 78.04 (No. of free parameters = 3)

As a model with lower AIC values is preferable thus now the order of models from best to worst:

MA(1) > AR(2) > ARMA(2,1)

Yes our conclusion change based on the criterion we use to assess models.

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