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

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

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

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defined by

*X _{t}*1 =

*Z*1 +

_{t},*.*8

*Z*

_{t}_{−1}

*,*1

*,*{

*Z*1} ∼ IID (0

_{t}*,σ*

^{2}

_{1})

*,*

and

*X _{t}*2 =

*Z*2 −

_{t},*.*6

*Z*

_{t}_{−1}

*,*2

*,*{

*Z*2} ∼ IID (0

_{t}*,σ*

^{2}

_{2})

*,*

where the two sequences {*Z _{t}*1} and {

*Z*2} are independent.

_{t}a. Find a large-sample approximation to the variance of *n*^{1}^{/}^{2} *h)*.

b. Find a large-sample approximation to the covariance of *n*^{1}^{/}^{2} *(h) *and

*n*^{1}^{/}^{2} *(k) *for *h *≠ *k*.