Rewrite the model using the backward shift operator b - is

Question

Let us assume that {W_t}_t is a white noise process with mean 0 and variance σ² = 1. Consider the time series {X_t}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 {Y_t}_t defined by:

stationary? Explain your answer.