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What I'm acquainted to is the AIC formula given in wikipedia, that is 

AIC=2k-2ln(L)

where k is the number of parameters and L is the maximized likelihood for a given model.

Whereas the AIC given in Matlab (see here) is 

AIC=N*log(det(1/N*sum_1^N(εε')))+2n_p+N*(n_y*(log(2π)+1))

where N is the number of values in the estimation data set, ε is a n_y by 1 vector of prediction errors, n_p is the number of estimated parameters (so it is equal to k in the first formulation) and n_y the number of model outputs.

Are these two formulae equivalent? If so, how to show the equivalence? One side question is what does n_y refer to?

Yimai
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    Matlab's formula is equivalent to the first one as long as the RVs are Gaussian. As for n_y, it refers to the number of outputs, i.e. the number of variables you are predicting. – RUser4512 Sep 14 '15 at 12:48
  • Thanks @RUser4512. How to derive that when the RVs are Gaussian, the first and third term in Matlab's formula is indeed -2ln(L)? As for n_y, in what circumstances, would we need to predict more than one dependent variable? I thought the dependent variable is always univariate, no? – Yimai Sep 14 '15 at 13:10

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