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

Details

The forecast error variance decomposition is based upon the orthogonalised impulse response coefficient matrices Ψ_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 σ_k^2(h), the resultant is a percentage figure. Formally:

σ_k^2(h) = ∑_{n=0}^{h-1}(ψ_{k1, n}^2 + … + ψ_{kK, n}^2)

which can be written as:

σ_k^2(h) = ∑_{j=1}^K(ψ_{kj, 0}^2 + … + ψ_{kj, h-1}^2) \quad.

Dividing the term (ψ_{kj, 0}^2 + … + ψ_{kj, h-1}^2) by σ_k^2(h) yields the forecast error variance decompositions in percentage terms.

Value

A list with class attribute ‘varfevd’ of length K holding the forecast error variances as matrices.

Author(s)

Bernhard Pfaff

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)