ex2-245b - Economics 245B Exercise 2 Consider the...

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Economics 245B Exercise 2 Consider the regression model Y t = X 0 t β + U t ,t =1 ,...,n in which X t and β are K 1 vectors. While the error is mean zero and i.i.d. unconditionally, U t exhibits conditional heteroskedasticity of the ARCH form U t = σ t V t , with V t iid N (0 , 1) and σ 2 t = α 0 + α 1 U 2 t 1 To ensure the conditional variance is positive, we impose the su cient condition α 0 > 0 and α 1 0 . a) Construct the likelihood function L ( β,α ) .H o w d ow e i m p o s e t h e c o n - straints? b) To avoid constrained optimization, one could replace ( α 0
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This note was uploaded on 12/26/2011 for the course ECON 245b taught by Professor Staff during the Fall '08 term at UCSB.

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