Rewrite the model using the shift operator b -nbsp is the

Question

Let us consider the ARMA time series {X_t}_t defined by:

where {W_t}_t is a white noise with variance one.

1. Rewrite the model using the shift operator B.

2. Is the model stationary? Say why.

3. Is the model invertible? Say why.

4. Express the model in an MA representation if it exists.

5. Express the model in an AR representation if it exists.