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T b 1 baxter king 2 where the constraint may or may

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Unformatted text preview: = 0 = �h −�l �j j=0 � Baxter-King Baxter and King (1999) proposed approximating the ideal filter with one of order J by solving �� 1 min |B (ei� − B � (ei� )|2 d� B () 2ω −� s.t. B (1) = β Baxter-King 2 where the constraint may or may not b e present. We might want to impose B (1) = 0 so that the filtered series is stationary, or if we’re constructing a low-pass filter, we might want B (1) = B (ei0 ) = 1 to preserve the lowest frequency movements. The Lagrangian is ⎤ �⎤ �∗ �� � � � 1 �B � (ei� − L= bj e−i�j ⎞ �B � (ei� − bj e−i�j ⎞ d� + �( bj − β) 2ω −� |j |�J |j |�J |j |�J The first order conditions are ⎤ � ⎤ �∗ �� �� � � 1 1 �B � (ei� − [bk ] : 0 = bj e−i�j ⎞ ei�k d� + e−i�k �B � (ei� − bj e−i�j ⎞ d� + � 2ω −� 2ω −� |j |�J |j |�J � [�] : 0 = ...
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This document was uploaded on 03/23/2014 for the course ECON 14.384 at MIT.

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