Computes the forecast error variance decomposition of a VAR(p) for
n.ahead steps.
Usage
## S3 method for class 'varest':
fevd(x, n.ahead=10, ...)
## S3 method for class 'svarest':
fevd(x, n.ahead=10, ...)
Arguments
x
Object of class varest; generated by
VAR(), or object of class svarest; generated by
SVAR().
n.ahead
Integer specifying the steps.
...
Currently not used.
Value
A list with class attribute varfevd of length K
holding the forecast error variances as matrices.
encoding
latin1
concept
VAR
Vector autoregressive model
fevd
forecast error variance decomposition
Details
The forecast error variance decomposition is based upon the
orthogonalised impulse response coefficient matrices $\Psi_h$ and
allow the user to analyse the contribution of variable $j$ to the
h-step forecast error variance of variable $k$. If the
orthogonalised impulse reponses are divided by the variance of the
forecast error $\sigma_k^2(h)$, the resultant is a percentage
figure. Formally:
$$\sigma_k^2(h) = \sum_{n=0}^{h-1}(\psi_{k1, n}^2 + \ldots + \psi_{kK, n}^2)$$
which can be written as:
$$\sigma_k^2(h) = \sum_{j=1}^K(\psi_{kj, 0}^2 + \ldots + \psi_{kj,
h-1}^2) \quad.$$
Dividing the term $(\psi_{kj, 0}^2 + \ldots + \psi_{kj, h-1}^2)$
by $\sigma_k^2(h)$ yields the forecast error variance
decompositions in percentage terms.
References
Hamilton, J. (1994), Time Series Analysis, Princeton
University Press, Princeton.
L�tkepohl, H. (2006), New Introduction to Multiple Time Series
Analysis, Springer, New York.