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Suppose that Xt=(X1t,X2t) and Xt=A1Xt1+A2Xt2+ut 1) In this question, assume that A2=0. For some instances, you cannot observe the original process and what you have
Suppose that Xt=(X1t,X2t) and Xt=A1Xt1+A2Xt2+ut 1) In this question, assume that A2=0. For some instances, you cannot observe the original process and what you have is Yt such that where vt=(ut,t)WN(0,(uuu)). (h.1) (2 points) Write down the VAR process with respect to Yt. (h.2) (3 points) Let the error term you obtained in (h.1) be denoted by vt. What is the mean, variance and the first order autocovariance of vt ? Is it White Noise? (h.3) (3 points) Obtain the covariance of Yt1 and vt. What does it imply? (h.4) (4 points) Can you figure out a way to consistently estimate A1 by using the autocovariance of Yt ? (Hint: you should satisfy the exogeneity condition.) Suppose that Xt=(X1t,X2t) and Xt=A1Xt1+A2Xt2+ut 1) In this question, assume that A2=0. For some instances, you cannot observe the original process and what you have is Yt such that where vt=(ut,t)WN(0,(uuu)). (h.1) (2 points) Write down the VAR process with respect to Yt. (h.2) (3 points) Let the error term you obtained in (h.1) be denoted by vt. What is the mean, variance and the first order autocovariance of vt ? Is it White Noise? (h.3) (3 points) Obtain the covariance of Yt1 and vt. What does it imply? (h.4) (4 points) Can you figure out a way to consistently estimate A1 by using the autocovariance of Yt ? (Hint: you should satisfy the exogeneity condition.)
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