Consider estimating the function t = r= a 0 r tr by a linear filter estimator of the form t = r=

Consider estimating the function

ψt =

Õ∞

r=−∞

a 0

r βt−r by a linear filter estimator of the form

ψˆ

t =

Õ∞

r=−∞

a 0

r βˆ

t−r, where βˆ

t is defined by (7.42). Show a sufficient condition for ψˆ

t to be an unbiased estimator; i.e., E ψˆ

t = ψt

, is H(ω)Z(ω) = I for all ω. Similarly, show any other unbiased estimator satisfying the above condition has minimum variance (see Shumway and Dean, 1968), so the estimator given is a best linear unbiased (BLUE) estimator.