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A Unique Orthogonal Variance Decomposition

Author

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  • Wong, Woon K

    (Cardiff Business School)

Abstract

Let e and &Sigma,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 = &Sigma, 1/2 , the square root of &Sigma,.

Suggested Citation

  • Wong, Woon K, 2008. "A Unique Orthogonal Variance Decomposition," Cardiff Economics Working Papers E2008/10, Cardiff University, Cardiff Business School, Economics Section.
    • Handle: RePEc:cdf:wpaper:2008/10
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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.

    More about this item

    Keywords

    Variance decomposition; Cholesky decomposition; unique orthogonal decomposition and square root matrix;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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