Suppose that yt follows the stationary AR(1) law of motion: Yt = 0 + 13t-1 +...
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Suppose that yt follows the stationary AR(1) law of motion: Yt = 0 + 13t-1 + Et, 1 < 1 (4) with E[yt-1&t] = 0 and is an iid sequence with Et~ N(0,02). Let y be another time series satisfying y = Yt + nt, where nt is a measurement error satisfying E(nt) = 0, Cov(nt, Es) = 0 and Cov(nt, ys) = 0 for all t and s, Var(t) = 1 and Cov(nt, ns) = 0 if t / s. Assume that, for any k, the sample autocovariances of yt or yt satisfy Ek+1 (at - a)(at-kā) →p Cov(at, at-k), where at = yt or yt. Compute E(yt) from (4) when do = 0.75, 1 = 0.5 and o² = 3. Compute Cor(yt, Yt-2) (the lag-two autocorrelation) from (4) when Po = 1, 1 = 0.5 and o² = 3. Compute Cor(yt, Yt-2) (the lag-two autocorrelation) from (4) when Po = 1, 1 = 0.5 and o² = 3. Suppose that yt follows the stationary AR(1) law of motion: Yt = 0 + 13t-1 + Et, 1 < 1 (4) with E[yt-1&t] = 0 and is an iid sequence with Et~ N(0,02). Let y be another time series satisfying y = Yt + nt, where nt is a measurement error satisfying E(nt) = 0, Cov(nt, Es) = 0 and Cov(nt, ys) = 0 for all t and s, Var(t) = 1 and Cov(nt, ns) = 0 if t / s. Assume that, for any k, the sample autocovariances of yt or yt satisfy Ek+1 (at - a)(at-kā) →p Cov(at, at-k), where at = yt or yt. Compute E(yt) from (4) when do = 0.75, 1 = 0.5 and o² = 3. Compute Cor(yt, Yt-2) (the lag-two autocorrelation) from (4) when Po = 1, 1 = 0.5 and o² = 3. Compute Cor(yt, Yt-2) (the lag-two autocorrelation) from (4) when Po = 1, 1 = 0.5 and o² = 3.
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To compute Eyt from equation 4 when 0 075 1 05 and 3 we substitute these values into the equat... View the full answer
Related Book For
Introduction to Econometrics
ISBN: 978-0133595420
3rd edition
Authors: James H. Stock, Mark W. Watson
Posted Date:
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