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Forecast Error Variance Decomposition

fevardec.Rd

Computes the Forecast Errors Variance Decomposition from a given (orthogonalized) impulse response function.

Usage

fevardec(obj, h.max = NULL, H = NULL)

Arguments

obj

impresp() object which represents the (orthogonalized) impulse response function.

h.max

maximum forecast horizon. The default is one plus the number of lags of the impresp object.

H

An (n x n) (non singular) matrix which renders the impulse response to a orthogonalized impulse response. The noise \(u_t\) is transformed to \(H^{-1}u_t\) and the impulse response coefficients (\(k_j \rightarrow k_j H\)) and the (left) square root of the noise covariance matrix (\(L \rightarrow H^{-1}L\)) are transformed correspondingly.
The default case H=NULL corresponds to the identity matrix (i.e. no transformation).
For H='chol', the transformation matrix H = t(chol(Sigma)) is obtained from the Choleski decomposition of the noise covariance \(\Sigma\). For H='eigen' the symmetric square root of \(\Sigma\) (obtained from the the eigenvalue decomposition of \(\Sigma\)) is used. For H='sigma_L' the left square root of the noise covariance, which is stored in the object obj, is used. Other orthogonalization schemes may be obtained by setting \(H\) to a suitable square root of \(\Sigma\).
The procedure checks whether the transformation yields an orthogonalized impulse response. If not, an error is thrown.

Value

fevardec object, i.e. a list with components

vd

n-by-n-by-h.max array which contains the forecast error variance decomposition: vd[i,j,h] is the percentage of the variance of the h-step ahead forecast error of the i-th component due to the j-th orthogonalized shock.

v

n-by-h.max matrix which contains the forecast error variances: v[i,h] is the variance of the h-step ahead forecast error for the i-th component.

names

(m)-dimensional character vector

label

character string or NULL

Examples

model = stspmod(sys = stsp(A = c(0,0.2,1,-0.5), B = c(1,1,1,-1),
                           C = c(1,0,0,1)),
                sigma_L = t(chol(matrix(c(4,2,2,3),nrow=2))),
                names = c('y1','y2'), label = 'test model')
fevardec(impresp(model, lag.max=10), H = 'chol', h.max = 5) %>% print(digits = 2, format = 'iz|j')
#> test model: Forecast error variance decompositon [2,2] maximum horizon = 5
#>        u[1] u[2]
#> h=1 y1 1.00 0.00
#>     y2 0.33 0.67
#> h=2 y1 0.87 0.13
#>     y2 0.33 0.67
#> h=3 y1 0.78 0.22
#>     y2 0.29 0.71
#> h=4 y1 0.74 0.26
#>     y2 0.27 0.73
#> h=5 y1 0.72 0.28
#>     y2 0.26 0.74
fevardec(impresp(model, lag.max=4, H = 'eigen'))            %>% print(digits = 2, format = 'iz|j')
#> test model: Forecast error variance decompositon [2,2] maximum horizon = 5
#>        u[1] u[2]
#> h=1 y1 0.92 0.08
#>     y2 0.11 0.89
#> h=2 y1 0.66 0.34
#>     y2 0.36 0.64
#> h=3 y1 0.65 0.35
#>     y2 0.31 0.69
#> h=4 y1 0.62 0.38
#>     y2 0.30 0.70
#> h=5 y1 0.60 0.40
#>     y2 0.30 0.70