Likelihood for Systems of Regression Equations * 1. Conditional, Marginal, and Concentrated Likelihoods
نویسنده
چکیده
We assume ε(t) | {X(s), y(s− 1), s ≤ t} ∼ N(0,Σ). This is the assumption that X(t) is predetermined in this system. In this notation, each equation (column of the system) has the same X(t) variable on the right-hand side and a distinct coefficient vector (column of B). However, we can consider versions of the system with 0 constraints on elements of B, which create different lists of variables in different equations, or with other linear restrictions on B, which might create links across B’s in different equations. The assumption of predetermined X(t) lets us write the pdf for the data at dates t = 1, . . . , T , conditional on {X(s), s ≤ 1} as
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