Let us assume that {Wt}t is a white noise process with mean 0 and variance σ2 = 1. Consider the time series {Xt}t defined by:
1. Rewrite the model using the backward shift operator B.
2. Is the model invertible? Say why.
3. Does an auto-regressive representation exist? If yes, give it.
4. Is the model stationary (causal)? Say why.
5. Does a moving average representation exist? If yes, give it.
6. Is the time series {Yt}t defined by:
stationary? Explain your answer.