R: Forecast Error Variance Decomposition

fevd {vars} | R Documentation

## 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`’; generated by `vec2var()`, or an object of class ‘`svecest`’; generated by `SVEC()`.
`n.ahead` | Integer specifying the steps.
`...` | Currently not used.

### 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)

[Package vars version 1.5-3 Index]