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Autocovariance and Autocorrelation of Moving Average Process

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**Please see the attached file for the complete problem description **

Please help me answer the attached exercise on independent random variables.

Let {X1} be the moving average process of order 2 given by

X1 = Z_t + theta(Z_t-2),

Where {Z_t} is WN (0, 1).

a) Find the auto covariance and the autocorrelation functions for this process when theta = .8

b) Compute the variance of the sample mean (X_1 + X_2 + X_3 + X_4)/4 when theta = .8

c) Repeat (b) when theta = -.8 and compare your answer with the result obtained in (b).

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Solution Summary

This solution guides you to calculate the autocovariance and autocorrelation of the order 2 moving average process. Also, the mean and the standard error of the special combination of Xt is calculated step by step.