rec05 - MIT OpenCourseWare http:/ocw.mit.edu 14.384 Time...

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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 .
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Variance Decomposition 1 14.384 Time Series Analysis, Fall 2007 Recitation by Paul Schrimpf Supplementary to lectures given by Anna Mikusheva October 5, 2007 Recitation 5 Variance Decomposition Suppose we have a VAR and we have some way to identify orthonormal shocks, so that y C ˜ t = ( L ) u t and Eu t u t = I k Impulse response functions let us report how y responds to changes in u . Another question we might ask is: how important is variation in u for explaining variation in y ? This question is addressed by reporting variance-decompositions. Then the error of the forecast of y t + s given all information up to time t is s y ˜ ˆ t + s | t y t + s = C s k u t + k k =1 So the MSE of the forecast is s MSE y ˜ ˜ y C I C of the shocks by looking at s C ˜ ˜ s k 1 jj C V ( s, j ) = ± k =1 s k MSE ( y ˆ t + s | t y t + s ) where 1 is a matrix of all zeros except for the j th diagonal element, which is one. V ( s, j ) is the portion of the variation in y at horizon s due to shock j . Table 1 shows a variance decomposition from Blanchard-Quah (1989).
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rec05 - MIT OpenCourseWare http:/ocw.mit.edu 14.384 Time...

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