Optimal weighting matrix continued New-West (1987)estimate of S could be correlated, the If the vector process h(o, y)- is serially S=+∑/(q+1)kr Where =170mr Why? varu]=q9E(u)+(g-1)E(u1)+E(u1)+.+E(x-1)+E(a11 g∑B(n)Optimal weighting matrix--- continued • If the vector process is serially correlated, the New-West (1987) estimate of S could be • Where • Why? • { } ∞ t t=−∞ h ( , y ) θ 0 { } ) ˆ ˆ 1 [ /( 1)] ( ˆ ˆ ' , , 1 0, v T v T q v T T S = Γ + ∑ − v q + Γ + Γ = ˆ 1 / {[ ( ˆ, )][ ( ˆ, )]' } 1 , t t v T t v v T T h y h y − = + Γ = ∑ θ θ ( ') var[ ] ( ) ( 1)[ ( ) ( )] ... [ ( ') ( ')] ' 1 ' 1 ' 1 t t k q v q t t t t t t t t q t q t q v v E u u q q v q u qE u u q E u u E u u E u u E u u − = − − − − − = ∑ ∑ − = = + − + + + +