Impulse Response Analysis — irf.varlse • bvhar

Computes responses to impulses or orthogonal impulses

Usage

# S3 method for class 'varlse'
irf(
  object,
  lag_max = 10,
  orthogonal = TRUE,
  impulse_var = NULL,
  response_var = NULL,
  ...
)

# S3 method for class 'vharlse'
irf(
  object,
  lag_max = 10,
  orthogonal = TRUE,
  impulse_var = NULL,
  response_var = NULL,
  ...
)

# S3 method for class 'bvarldlt'
irf(
  object,
  lag_max = 10,
  orthogonal = TRUE,
  impulse_var = NULL,
  response_var = NULL,
  level = 0.05,
  num_thread = 1,
  sparse = FALSE,
  med = FALSE,
  ...
)

# S3 method for class 'bvharldlt'
irf(
  object,
  lag_max = 10,
  orthogonal = TRUE,
  impulse_var = NULL,
  response_var = NULL,
  level = 0.05,
  num_thread = 1,
  sparse = FALSE,
  med = FALSE,
  ...
)

# 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
level: Specify alpha of confidence interval level 100(1 - alpha) percentage. By default, .05.
num_thread: Number of threads
sparse: Apply restriction. By default, FALSE. Give CI level (e.g. .05) instead of TRUE to use credible interval across MCMC for restriction.
med: If TRUE, use median of forecast draws instead of mean (default).
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.