Let us assume that θ ∈ (-1, +1) is known, that {Wt} is a Gaussian white noise with variance one, and that
is a Gaussian white noise with variance θ2. Show that the MA(1) time series {Xt}t defined by:
![](https://book.transtutors.com/qimg/af8565b6-ece8-4c8e-abd1-ad034af38cc5.png)
Show that the MA(1) time series {Xt}t defined by:
![](https://book.transtutors.com/qimg/cd6550a6-f69f-4044-9244-72ecbc38bfe2.png)
have the same auto-covariance functions. Do they have the same auto-correlation functions?