recitation3 notes

The baxter king lter can b e considered a special

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Unformatted text preview: 0 j=0 � � 1� � β− �j ⎞ 2J + 1 |j |�J Christiano-Fitzgerald 3 Christiano-Fitzgerald Christiano and Fitzgerald (1999) propose a generalization of the Baxter-King filter. The advocate choosing a finite approximation to the ideal filter by solving min E [(Bt (L)xt − B � (L)xt )2 ] Bt () where xt is some chosen process. Bt (L) is allowed to use all data available in your sample of length T . Note that Bt (L) will generally not b e symmetric and will change with t. As shown in problem set 1, this is equivalent to solving, �� 1 min |Bt (ei� ) − B � (ei� )|2 Sx (� )d� Bt () 2ω −� where Sx (� ) is the spectrum of xt . The Baxter-King filter can b e considered a special case of this approach where xt is white noise, a...
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This document was uploaded on 03/23/2014 for the course ECON 14.384 at MIT.

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