vars (version 1.6-1)

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, ...)

Value

A list with class attribute ‘varfevd’ of length K

holding the forecast error variances as matrices.

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.

Author

Bernhard Pfaff

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.

Lütkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

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

Examples

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