Time series

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Gnanf

Mathematics

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2. Suppose Yt = u +01€-1 +02€t-2 + €t where Et are iid N(0,02) random variables (see HW#1, Problem #3 for details). Using the results from problem #1 above, find Var(7). Compare your answer to what would have been obtained if Yt = 4 + €t. Describe the effect that the autocorrelation, namely pi and P2, in {Y{} has on Var(Y). 3. Let X have a distribution with mean y and variance oʻ, neither of which depends on t. Let Yt = X for all t. (a) Show that {Y{} is strictly stationary. (b) Show that {Y{} weakly stationary using the definition (i.e., it is both mean and covariance stationary). Do not use the argument that strictly stationary implies weakly stationary. (c) Sketch a "typical” time plot for Yt.
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