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psvii245b - Such a nonstationary series is termed...

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University of California D. Steigerwald Department of Economics Economics 245B Problem Set VII 1. For the MA(1) process Y t = ε t + θε t-1 , where θ < 1 and ε t IN(0, σ 2 ), show how you would estimate θ under the following situations: a. Approximate MLE b. Exact MLE c. Exact MLE using the Kalman Filter 2. Show that the following random walk process with drift y t = y t-1 + d + ε t , with E( ε t ) = 0 and E( ε t ε s ) = 0 for t s, is first-order homogeneous nonstationary. Note: Many of the nonstationary time series have the property that if they are differenced one or more times, the resulting series will be stationary.
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Unformatted text preview: Such a nonstationary series is termed homogeneous. The number of times that the original series must be differenced before a stationary series results is called the order of homogeneity. 3. Consider the model y t = α + ε t ε t = ρε t-1 + u t , where ρ < 1 and {u t } is an i.i.d. sequence with known density g(u t ) that is centered at the origin. Show that the OLS estimator of α is unbiased and consistent. Derive the bias in the OLS standard errors and show the direction of the bias when ρ > 0....
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