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Question: consider the following ma2 process zt ut 1ut1...

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Consider the following MA(2) process: zt = ut + α1ut1 + α2ut2, where ut is a zero-mean white noise process with variance σ2.

(a) Calculate the conditional and unconditional means of zt, that is, Et[zt+1] and E[zt]. 

(b) Calculate the conditional and unconditional variances of zt, that is, Vart[zt+1] and Var[zt]. 

(c) Derive the autocorrelation function of this process for all lags as functions of the parameters α1 and α2

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