6.11 In §6.3, we discussed that it is possible to obtain a recursion for the gradient vector, −∂ lnLY (Θ)/∂Θ. Assume the model is given by (6.1)

and (6.2) and At is a known design matrix that does not depend on Θ, in which case Property P6.1 applies. For the gradient vector, show

where the dependence of the innovation values on Θ is understood. In addition, with the general definition ∂ig = ∂g(Θ)/∂Θi, show the following recursions, for t = 2, . . . , n apply:

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a 1n Ly ()/201 {' + 77 -1 ;)}.