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:
Show that the MA(1) time series {Xt}t defined by:
have the same auto-covariance functions. Do they have the same auto-correlation functions?