Unformatted text preview: Write down the sample periodogram estimator. Show that this estimator is asymptotically unbiased. Is it possible to have an estimator that is asymptotically unbiased but not consistent? Explain. 2b. How could the sample periodogram estimator be used to estimate the covariance matrix? Can we separately identify each of the elements in the matrix? Describe any potential problems with the sample periodogram estimator and how to construct a new estimator to overcome them. 3. Give the theoretical autocovariance and autocorrelation functions for the following two MA processes y t = (1  .5L) ε t y t = (1 + 0.5L + 0.4L 2 ) ε t where ε t ∼ iid(0,1)...
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 Fall '08
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 Economics, Variance, spectral density, Estimation theory, D. Steigerwald, sample periodogram estimator

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