Consider a m-vector linear process

where are i.i.d. m-vector random variables with p.d.f. on , are matrices depending on a parameter vector .

Set

Assume the following conditions are satisfied

**A1** i) For some

where denotes the sum of the absolute values of the entries of .

ii) Every is continuously two times differentiable with respect to , and the derivatives satisfy

for where .

iii) for and can be expanded as follows:

where , satisfy

iv) Every is continuously two times differentiable with respect to , and the derivatives satisfy

for

**A2** satisfies

**A3** The continuous derivative of exists on .

**A4**

where .

From A1 the linear process can be expressed as

and hence

where

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