Let xt be an ARMA(p2; q2) process and let yt be an ARMA(p2; q2) process, such that xt, yt are independent. De_ne zt = xt + yt. Verify that zt is an ARMA(p; q) process such that p _ p1+p2 and q _...

Let xt be an ARMA(p2; q2) process and let yt be an ARMA(p2; q2)

process, such that xt, yt are independent. De_ne zt = xt + yt. Verify that zt

is an ARMA(p; q) process such that p _ p1+p2 and q _ maxfp1+q2; q1+p2g.

If an ARMA(p; q) model with p > 0 and q > 0 is stationary, then

provide conditions such that

(a) It is also invertible.

(b) It can be written as an in_nite-order MA model.

(c) It can be written as a _nite-order MA model.

(d) It can be written as a _nite-order AR model