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Question: consider the zeromean ma1 process xt xt ut ...

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Consider the zero-mean MA(1) process Xt:

Xt = ut + δut−1 where ut i.i.d ∼ N(0, σ2 u ).

(a) Find E[Xt], Et[Xt+1], Et[Xt+2].

(b) Find γ0 = Var[Xt]. 

(c) Derive the autocorrelation function (ACF). Now, imagine you have a parameter estimate of δ = 0.70. Plot the autocorrelation function as a function of the number of lags.

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