Let {X t } be the bivariate time series whose components are the MA(1) processesdefined by Xt 1 =Zt,1 +.8Zt −1 ,1,{Zt 1} ∼ IID (0,σ 2 1),and Xt 2 =Zt,2 −.6Zt −1 ,2,{Zt 2} ∼ IID (0,σ 2 2),where the two sequences {Zt 1} and {Zt 2} are independent.a. Find a large-sample approximation to the variance ofn 1 / 2 h).b. Find a large-sample approximation to the covariance ofn 1 / 2(h)and n 1 / 2(k)forh≠k.

Let {X t } be the bivariate time series whose components are the MA(1) processes defined by X t 1 = Z t , 1 + . 8 Z t −1 , 1 , { Z t 1} ∼ IID (0 ,σ 2 1 ) , and X t 2 = Z t , 2 − . 6 Z t −1 , 2 , { Z t...

Let {X
_t
} be the bivariate time series whose components are the MA(1) processes

defined by

X_t
1 =Z_t,1 +.8Z_t

₋₁
,1,{Z_t
1} ∼ IID (0,σ
²
₁),

and

X_t
2 =Z_t,2 −.6Z_t

₋₁
,2,{Z_t
2} ∼ IID (0,σ
²
₂),

where the two sequences {Z_t
1} and {Z_t
2} are independent.

a. Find a large-sample approximation to the variance ofn
¹

^/

²
h).

b. Find a large-sample approximation to the covariance ofn
¹

^/

²(h)and

n
¹

^/

²(k)forh≠k.

May 25, 2022