Computes responses to impulses or orthogonal impulses
Usage
# S3 method for class 'varlse'
irf(object, lag_max = 10, orthogonal = TRUE, impulse_var, response_var, ...)
# S3 method for class 'vharlse'
irf(object, lag_max = 10, orthogonal = TRUE, impulse_var, response_var, ...)
# S3 method for class 'bvharirf'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
irf(object, lag_max, orthogonal, impulse_var, response_var, ...)
is.bvharirf(x)
# S3 method for class 'bvharirf'
knit_print(x, ...)Arguments
- object
Model object
- lag_max
Maximum lag to investigate the impulse responses (By default,
10)- orthogonal
Orthogonal impulses (
TRUE) or just impulses (FALSE)- impulse_var
Impulse variables character vector. If not specified, use every variable.
- response_var
Response variables character vector. If not specified, use every variable.
- ...
not used
- x
Any object
- digits
digit option to print
Value
bvharirf class
Responses to forecast errors
If orthogonal = FALSE, the function gives \(W_j\) VMA representation of the process such that
$$Y_t = \sum_{j = 0}^\infty W_j \epsilon_{t - j}$$
Responses to orthogonal impulses
If orthogonal = TRUE, it gives orthogonalized VMA representation $$\Theta$$.
Based on variance decomposition (Cholesky decomposition)
$$\Sigma = P P^T$$
where \(P\) is lower triangular matrix,
impulse response analysis if performed under MA representation
$$y_t = \sum_{i = 0}^\infty \Theta_i v_{t - i}$$
Here,
$$\Theta_i = W_i P$$
and \(v_t = P^{-1} \epsilon_t\) are orthogonal.
References
Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis. Springer Publishing.