A mvgam_fevd object returned by function fevd(). Run
methods(class = "mvgam_fevd") to see an overview of available methods.
Details
A forecast error variance decomposition is useful for quantifying
the amount of information each series that in a Vector Autoregression
contributes to the forecast distributions of the other series in the
autoregression. This object contains the forecast error variance
decomposition using the orthogonalised impulse response coefficient
matrices \(\Psi_h\), which can be used to quantify the contribution of
series \(j\) to the h-step forecast error variance of series \(k\):
$$
\sigma_k^2(h) = \sum_{j=1}^K(\psi_{kj, 0}^2 + \ldots + \psi_{kj,
h-1}^2) \quad
$$
If the orthogonalised impulse reponses \((\psi_{kj, 0}^2 + \ldots +
\psi_{kj, h-1}^2)\) are divided by the variance of the forecast error
\(\sigma_k^2(h)\), this yields an interpretable percentage representing
how much of the forecast error variance for \(k\) can be explained by an
exogenous shock to \(j\). This percentage is what is calculated and
returned in objects of class mvgam_fevd, where the posterior
distribution of variance decompositions for each variable in the original
model is contained in a separate slot within the returned list object