A unique orthogonal variance decomposition - Woon K. Wong (Cardiff University, Cardiff Business School, 2008)
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[...] , the square root of Σ.
Keywords: C01; 330; Variance decomposition; Cholesky decomposition; unique orthogonal decomposition and square root matrix; Varianzanalyse; Statistische Methode