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A Unique Orthogonal Variance Decomposition

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  • Wong, Woon K

    ()
    (Cardiff Business School)

Abstract

Let e and Σ be respectively the vector of shocks and its variance covariance matrix in a linear system of equations in reduced form. This article shows that a unique orthogonal variance decomposition can be obtained if we impose a restriction that maximizes the trace of A, a positive definite matrix such that Az = e where z is vector of uncorrelated shocks with unit variance. Such a restriction is meaningful in that it associates the largest possible weight for each element in e with its corresponding element in z. It turns out that A = Σ 1/2 , the square root of Σ.

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Bibliographic Info

Paper provided by Cardiff University, Cardiff Business School, Economics Section in its series Cardiff Economics Working Papers with number E2008/10.

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Length: 19 pages
Date of creation: Apr 2008
Date of revision:
Handle: RePEc:cdf:wpaper:2008/10

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Keywords: Variance decomposition; Cholesky decomposition; unique orthogonal decomposition and square root matrix;

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Cited by:
  1. Clatworthy, Mark A & Pong, Christopher K.M. & Wong, Woon K., 2009. "Auditor Quality and the Role of Accounting Information in Explaining UK Stock Returns," Cardiff Economics Working Papers E2009/9, Cardiff University, Cardiff Business School, Economics Section, revised Oct 2011.

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