irf: Impulse response function

In vars: VAR Modelling

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’; generated by vec2var(), or object of class ‘svecest’; generated by SVEC().
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.

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.

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)’.

Author(s)

Bernhard Pfaff

References

Efron, B. and R. J. Tibshirani (1993), An Introduction to the Bootstrap, Chapman and Hall, New York.

Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton.

Lütkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

VAR, SVAR, 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, estmethod = "direct", Amat = amat)
irf(svar.a, impulse = "e", response = c("prod", "rw", "U"), boot =
FALSE)

vars documentation built on March 31, 2023, 10:30 p.m.