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Unformatted text preview: Be explicit in setting up the problem and carefully explain the steps. b. Is there measurement error in this problem? If so, where? c. What are the advantages to using the Kalman filter? d. How does the Kalman filter compare to exact maximum likelihood estimation? e. Once you have an estimate of θ , how would you forecast y t+n ? 3. Consider the VAR(1) model given by: Y t = Φ Y t-1 + ε t t = 1,. ..,T ε t ∼ Multivariate independent Normal (Q, Ω ) . a. Describe in detail, including the likelihood function, how you would estimate Φ using Approximate MLE. You may assume y 1 ~ IN(0 , Σ ) where vec I vec N ( ) ( ) ( ). Σ Φ Φ Ω =-⊗-2 1 b. Describe in detail how you would estimate Φ using Exact MLE. c. Discuss any other “useful” approach to estimating Φ ....
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- Fall '08
- Economics, Maximum likelihood, Estimation theory, Likelihood function, Department of Economics, Kalman filter, D. Steigerwald