The bivariate MA(4) model (boldsymbol{x}_{t}=boldsymbol{a}_{t}-boldsymbol{Theta}_{4} boldsymbol{a}_{t-4}) is another seasonal model with periodicity 4 , where (left{boldsymbol{a}_{t} ight})

The bivariate MA(4) model \(\boldsymbol{x}_{t}=\boldsymbol{a}_{t}-\boldsymbol{\Theta}_{4} \boldsymbol{a}_{t-4}\) is another seasonal model with periodicity 4 , where \(\left\{\boldsymbol{a}_{t}\right\}\) is a sequence of independent and identically distributed normal random vectors with mean zero and covariance matrix \(\boldsymbol{\Sigma}\). Derive the covariance matrices \(\boldsymbol{\Gamma}_{\ell}\) of \(\boldsymbol{x}_{t}\) for \(\ell=0, \ldots, 5\).