exam - MIT OpenCourseWare http://ocw.mit.edu 14.384 Time...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 14.384 Time Series Analysis Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 14.384: Time Series Analysis. Final Exam. due Wednesday, December 19 (1:30PM - 4:30PM) You may turn it in earlier by sending me an e-mail or stopping by my office. The exam should take you approximately 3 hours. Late works will not be accepted. Good luck! 1. Posterior for variance of normals. The Inverse-chi-square distribution IG ( ν,σ 2 ) has density: 2 2 p ( x | ν 2 ( σ ν/ 2) ν/ ,σ ) = σ x- (1+ ν/ 2) exp Γ( ν/ 2) ‰ 2 ν- , 2 x x ≥ ,ν > , with ν being the degrees of freedom and σ 2 being the scale parameter. It has mean σ 2 ν 2 for ν > 2 and variance 2 ν σ 4 ν- 2 for ( ν- 2) 2 ν > 4. ( ν- 4) Consider an iid sample Y T = { y 1 ,...,y T } from N ( μ,σ 2 ). (i) Assume that the prior has the following convenient parametrization: 2 μ | σ 2 σ ∼ N ( μ , ) , and σ 2 ∼ IG ( ν ,σ 2...
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exam - MIT OpenCourseWare http://ocw.mit.edu 14.384 Time...

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