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Determine the auto covariance and the autocorrelation


Question: Let {Xt} be the MA(1) process

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Xt = Zt + ΘZt-2  with  Zt ~ WN(0, σ2).

(i) Determine the auto covariance and the autocorrelation function of {Xt} for θ = 0:9.

(ii) Determine the variance of the mean (X1 + X2 + X3 + X4)/4.

(iii) How do the previous results change if θ = 0:9?

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Macroeconomics: Determine the auto covariance and the autocorrelation
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