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Suppose time-series data has been generated according to the following process:
where t is independent white noise. Our main interest is consistent estimation of Φ from realizations on yt.
1) Provide conditions for this process to be stationary.
2) From hereonout, assume the process is stationary. Will OLS generally provide you with consistent point estimates of ? Can you give conditions under which it will? Provide the asymptotic distribution of OLS under these assumptions.
3) ARMA processes are generally estimated by ML. Do you have enough information to set up the (marginal or conditional) likelihood function?
4) Use the moment conditions under Question 4 to derive a consistent GMM estimator of (; ).
Does it require knowledge of the distribution of t? Note that we discussed asymptotic properties
of GMM estimators assuming a xed amount of moments.
5) Given your answer to the previous question, derive a lower bound on the variance of your esti-
mator.
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The following table contains the ACT scores and the GPA (grade point average) for eight college students. Grade point average is based on a four-point scale and has been rounded to
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Consider the following equations designed to estimate a school's test scores (Test) and the school's dropout rate (Drop). Test i = B 0 + B 1 *Parent Ed i + B 2 *school quali
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