vars (version 1.1-9)

fevd: Forecast Error Variance Decomposition

Description

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, ...)
## S3 method for class 'svecest':
fevd(x, n.ahead=10, ...)
## S3 method for class 'vec2var':
fevd(x, n.ahead=10, ...)

Arguments

x

Object of class varest; generated by VAR(), or an object of class svarest; generated by SVAR(), or an object of class vec2var

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
• VECM

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.

See Also

VAR, SVAR, SVAR2, vec2var, SVEC, Phi, Psi, plot

Examples

data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
fevd(var.2c, n.ahead = 5)