Midterm part 1

Midterm part 1 - t =Z t + bZ t-3 , (1) where Zt ~ WN(0,1)....

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1. If X t and Y t are uncorrelated (weakly) stationary sequences, i.e., if X r and Y s are uncorrelated for every r and s, show that X t +Y t is (weakly) stationary with autocovariance function equal to the sum of the autocovariance functions of X t and Y t . Let W t = X t +Y t , Uncorrelated = indepedent 2. Let {Xt} satisfy the equation X
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Unformatted text preview: t =Z t + bZ t-3 , (1) where Zt ~ WN(0,1). Such an equation (1) is called a moving-average model of order 3, or an MA(3) model. a) Find the autocovariance functions of X t when b=-0.6; b) Find the autocorrelation functions of X t when b=-0.6....
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