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

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This note was uploaded on 03/20/2012 for the course 14 14.02 at MIT.

### Page1 / 3

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online