The VAR model is modified in such a way that contemporaneous correlation among the residuals is diagonal, called

orthogonalisation.

In addition, the WCAWE introduces correction factors in the

orthogonalisation process to ensure that the techniques preserve the moments of the original system.

Since the preconditioning operation is adaptive, the standard CG method has been replaced by an economic version of the conjugate gradient algorithm with explicit

orthogonalisation of the search directions called "flexible conjugate gradients;" see Notay [18].

This can be carried out, for instance, by External Parameter Orthogonalisation (EPO) (Roger et al.

Roger JM, Chauchard F, Bellon-Maurel V (2003) EPO-PLS external parameter orthogonalisation of PLS application to temperature-independent measurement of sugar content of intact fruits.

beta]](x) after image filtering by FCA, data reduction by model fitting and parameters

orthogonalisation by PCA.

The difference between our study and the work of Fidrmuc and Korhonen (2003) and Dibooglu and Kutan (2001) is that these authors rely on the Blanchard-Quah identification that is stronger than the GCP restriction and the

orthogonalisation that we use.

The upper panel shows the eigenvalues from the orthogonalisation of the sample correlation matrix and how much each principal component explains of the total variance of the primary EBRD indices (found as the eigenvalue of each principal component divided by the sum of eigenvalues).

The eigenvalues from the orthogonalisation reflect the share of total variation explained by each principal component.

Unlike the traditional impulse response analysis, this approach--referred to as generalised impulse response analysis--does not require orthogonalisation of shocks and is invariant to the ordering of the variables in the VAR.

Unlike the traditional impulse response analysis, this approach does not require orthogonalisation of shocks and is invariant to the ordering of the variables in the VAR.

The transformations include a robust process of nonunitary

orthogonalisation in the metric of a symmetric positive-definite matrix.