vars (version 1.1-9)

irf: Impulse response function

Description

Computes the impulse response coefficients of a VAR(p) (or transformed VECM to VAR(p)) or a SVAR for n.ahead steps.

Usage

## S3 method for class 'varest':
irf(x, impulse = NULL, response = NULL, n.ahead = 10,
ortho = TRUE, cumulative = FALSE, boot = TRUE, ci = 0.95,
runs = 100, seed = NULL, ...)
## S3 method for class 'svarest':
irf(x, impulse = NULL, response = NULL, n.ahead = 10,
ortho = TRUE, cumulative = FALSE, boot = TRUE, ci = 0.95,
runs = 100, seed = NULL, ...)
## S3 method for class 'vec2var':
irf(x, impulse = NULL, response = NULL, n.ahead = 10,
ortho = TRUE, cumulative = FALSE, boot = TRUE, ci = 0.95,
runs = 100, seed = NULL, ...)
## S3 method for class 'svecest':
irf(x, impulse = NULL, response = NULL, n.ahead = 10,
ortho = TRUE, cumulative = FALSE, boot = TRUE, ci = 0.95,
runs = 100, seed = NULL, ...)

Arguments

x

Object of class varest; generated by VAR(), or object of class svarest; generated by SVAR(), or object of class vec2var

impulse

A character vector of the impulses, default is all variables.

response

A character vector of the responses, default is all variables.

n.ahead

Integer specifying the steps.

ortho

Logical, if TRUE (the default) the orthogonalised impulse response coefficients are computed (only for objects of class varest).

cumulative

Logical, if TRUE the cumulated impulse response coefficients are computed. The default value is false.

boot

Logical, if TRUE (the default) bootstrapped error bands for the imuplse response coefficients are computed.

ci

Numeric, the confidence interval for the bootstrapped errors bands.

runs

An integer, specifying the runs for the bootstrap.

seed

An integer, specifying the seed for the rng of the bootstrap.

...

Currently not used.

Value

• A list of class varirf with the following elements is returned:
• irf
  A list with matrices for each of the impulse variables containing the impulse response coefficients.
• Lower
  If boot = TRUE, a list with matrices for each of the impulse variables containing the lower bands.
• Upper
  If boot = TRUE, a list with matrices for each of the impulse variables containing the upper bands.
• response
  Character vector holding the names of the response variables.
• impulse
  Character vector holding the names of the impulse variables.
• ortho
  Logical, if TRUE, orthogonalised impulse reponses have been computed.
• cumulative
  Logical, if TRUE, cumulated impulse reponses have been computed.
• runs
  An integer, specifying the number of bootstrap runs.
• ci
  Numeric, defining the confidence level.
• boot
  Logical, if TRUE bootstrapped error bands have been computed.
• model
  Character, containing class(x).

encoding

latin1

concept

• VAR
• SVAR
• Vector autoregressive model
• Structural vector autoregressive model
• irf
• impulse response function
• VECM

Details

The impulse response coefficients of a VAR(p) for n.ahead steps are computed by utilising either the function Phi() or Psi(). If boot = TRUE (the default), confidence bands for a given width specified by ci are derived from runs bootstrap. Hereby, it is at the users leisure to set a seed for the random number generator. The standard percentile interval is defined as: $$CI_s = [s_{\alpha/2}^*, s_{1 - \alpha/2}^*] \quad ,$$ with $s_{\alpha/2}^*$ and $s_{1 - \alpha/2}^*$ are the $\alpha/2$ and $1 - \alpha/2$ quantiles of the bootstrap distribution of $\Psi^*$ or $\Phi^*$ depending whether ortho = TRUE. In case cumulative = TRUE, the confidence bands are calculated from the cumulated impulse response coefficients.

References

Efron, B. and R. J. Tibshirani (1993), An Introduction to the Bootstrap, Chapman & Hall, New York. Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton. L�tkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

VAR, SVAR, SVAR2, vec2var, SVEC, Phi, Psi, plot

Examples

data(Canada)
## For VAR
var.2c <- VAR(Canada, p = 2, type = "const")
irf(var.2c, impulse = "e", response = c("prod", "rw", "U"), boot =
FALSE)
## For SVAR
amat <- diag(4)
diag(amat) <- NA
svar.a <- SVAR(var.2c, Amat = amat)
irf(svar.a, impulse = "e", response = c("prod", "rw", "U"), boot =
FALSE)