Show that the ma1 time series xttnbspdefined by given, Financial Econometrics

Show that the ma1 time series xttnbspdefined by given

Let us assume that θ ∈ (-1, +1) is known, that {W_t} 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 {X_t}_t defined by:

Show that the MA(1) time series {X_t}_t defined by:

have the same auto-covariance functions. Do they have the same auto-correlation functions?

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Financial Econometrics: Show that the ma1 time series xttnbspdefined by given

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