ABSTRACT
DenotebyL~',~theGaussianlikelihoodobtainedbysubstitutinga .V(0,0"2)densityforfinEq.(1.7),andconsiderthederivatives,withrespect to9,oftheresultingGaussianlog-likelihood
11 -1/2II =- -,-,LZ 1(9)grad9(Z1(9))+op(I)
~Ll~;;~,(2.1) wherea~~n-1:L;'= 1z?(9).Inthepresentcase,Eq.(1.6)yields
grad9 (Z,(9))=grads(X1 - tt9iXt-i) =-(Xt-I,...,X1-p) 1,(2.2)
sothat
underH}")(9)asn->oowherefisanydensitysuchthat Jxf(x)dx=0andJx2f(x)dx~·0"2<oo.(2.4)
Theasymptoticcovariancematrixf,1 (9)istheautocovariancematrixof orderpofthestationaryAR(p)solutionofEq.(l.l)understandardnormal innovations;namely,denotingbyg 11 (9)theGreen'sfunctionsassociated with(1.1),characterizedby
