Suppose (Y_{t}) follows a random walk, (Y_{t}=Y_{t-1}+u_{t}), for (t=1, ldots, T), where (Y_{0}=0) and (u_{t}) is i.i.d.
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Suppose \(Y_{t}\) follows a random walk, \(Y_{t}=Y_{t-1}+u_{t}\), for \(t=1, \ldots, T\), where \(Y_{0}=0\) and \(u_{t}\) is i.i.d. with mean 0 and variance \(\sigma_{u}^{2}\).
a. Compute the mean and variance of \(Y_{t}\).
b. Compute the covariance between \(Y_{t}\) and \(Y_{t-\mathrm{k}}\).
c. Use the results in (a) and (b) to show that \(Y_{t}\) is nonstationary.
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