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