where it is treated as a constant in the integration, Θ is a vector of parameters, and T is the number of observations. The Akaike Information Criterion is the predictor of W and can be expressed as(1.11)
where p is the dimension of vector α. The objective is to find the specification that minimizes the AIC. See Amemiya ( 1985) for a discussion of the use of the Akaike Information Criterion.