The three models AR(2), MA(1), and ARMA(2, 1) are fitted to the following time s

Question

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). Redo problem 2 using Akaike Information Criterion Corrected for bias (AICC) (see sect 11.3 of Lecture Notes Lecture 12). Did your conclusions change?

Explanation / Answer

Lower AIC is better. SO order of models from best to worst is MA(1), AR(2), ARMA(2,1)

3. AIC corrected for bias is -2*LL + 2*No of free parameters*(n/(n-No of free parameters-1))

Hence we get the following table

So, conclusion still remains the same

Model Log likelihood Free parameters AIC AR(2) -36.4 3 78.8 MA(1) -36.51 2 77.02 ARMA(2,1) -36.02 4 80.04

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