vars (version 1.5-3)

fevd: Forecast Error Variance Decomposition

Description

Computes the forecast error variance decomposition of a VAR(p) for n.ahead steps.

Usage

# S3 method for varest
fevd(x, n.ahead=10, ...)
# S3 method for svarest
fevd(x, n.ahead=10, ...)
# S3 method for svecest
fevd(x, n.ahead=10, ...)
# S3 method for 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’; generated by vec2var(), or an object of class ‘svecest’; generated by SVEC().

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.

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<U+34AE5C2F>hl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

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

Examples

# NOT RUN {
data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
fevd(var.2c, n.ahead = 5)
# }