Consider estimating the function t = X r= a0 rtr by a linear filter estimator of the form bt = X r= a0 rbtr, where

Consider estimating the function

ψt = X∞

r=−∞

a0 rβt−r by a linear filter estimator of the form

ψbt = X∞

r=−∞

a0 rβbt−r, where βbt is defined by (7.42). Show a sufficient condition for ψbt to be an unbiased estimator; i.e., E ψbt = 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.