The fraction of the h-step forecast error variance of each variable
attributable to each orthogonalised shock. With P the lower Cholesky
factor of Sigma_u and Theta_s = A^s the MA coefficients of a VAR(1),
the h-step MSE contribution of shock j to variable i is
sum_{s=0}^{h} (Theta_s P)[i, j]^2, and the decomposition divides that
by the row total.
Usage
Fevdc(var_coefficients, sigma_u, periods = 20)
Arguments
- var_coefficients
VAR(1) coefficient matrix A (k by k).
- sigma_u
Residual covariance matrix (k by k).
- periods
Forecast horizon.
Value
List with decomposition (a (periods+1) by k by k array),
mse_contributions, periods, k.
Details
R mirror of morie.fn.fevdc; the Python arm carries the primary
documentation.
References
Lutkepohl, H. (2005). New Introduction to Multiple Time
Series Analysis. Springer. doi:10.1007/978-3-540-27752-1.
Examples
Fevdc(matrix(c(0.5, 0.1, 0.2, 0.4), 2, 2), diag(2), 3)$decomposition[4, , ]
#> [,1] [,2]
#> [1,] 0.93846583 0.06153417
#> [2,] 0.01805133 0.98194867
