irf.varlse: Impulse Response Analysis

Description

Computes responses to impulses or orthogonal impulses

Usage

# S3 method for varlse
irf(object, lag_max = 10, orthogonal = TRUE, impulse_var, response_var, ...)
# S3 method for vharlse
irf(object, lag_max = 10, orthogonal = TRUE, impulse_var, response_var, ...)
# S3 method for bvharirf
print(x, digits = max(3L, getOption("digits") - 3L), ...)
irf(object, lag_max, orthogonal, impulse_var, response_var, ...)
is.bvharirf(x)
# S3 method for bvharirf
knit_print(x, ...)

Value

bvharirf

class

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

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.