Determine the auto covariance and the autocorrelation, Macroeconomics

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Determine the auto covariance and the autocorrelation

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

X_t = Z_t + ΘZ_t-2 with Z_t ~ WN(0, σ²).

(i) Determine the auto covariance and the autocorrelation function of {X_t} 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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Macroeconomics: Determine the auto covariance and the autocorrelation

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