Computes the impulse response coefficients of a VAR(p) (or transformed
VECM to VAR(p)) or a SVAR for n.ahead steps.
# S3 method for 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 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 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 svecest
irf(x, impulse = NULL, response = NULL, n.ahead = 10,
ortho = TRUE, cumulative = FALSE, boot = TRUE, ci = 0.95,
runs = 100, seed = NULL, ...)A list of class ‘varirf’ with the following elements is
returned:
A list with matrices for each of the impulse variables containing the impulse response coefficients.
If boot = TRUE, a list with matrices for each of
the impulse variables containing the lower bands.
If boot = TRUE, a list with matrices for each of
the impulse variables containing the upper bands.
Character vector holding the names of the response variables.
Character vector holding the names of the impulse variables.
Logical, if TRUE, orthogonalised impulse reponses
have been computed.
Logical, if TRUE, cumulated impulse reponses
have been computed.
An integer, specifying the number of bootstrap runs.
Numeric, defining the confidence level.
Logical, if TRUE bootstrapped error bands have been
computed.
Character, containing ‘class(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().
A character vector of the impulses, default is all variables.
A character vector of the responses, default is all variables.
Integer specifying the steps.
Logical, if TRUE (the default) the orthogonalised impulse
response coefficients are computed (only for objects of class
‘varest’).
Logical, if TRUE the cumulated
impulse response coefficients are computed. The default value is false.
Logical, if TRUE (the default) bootstrapped error
bands for the imuplse response coefficients are computed.
Numeric, the confidence interval for the bootstrapped errors bands.
An integer, specifying the runs for the bootstrap.
An integer, specifying the seed for the rng of the
bootstrap.
Currently not used.
Bernhard Pfaff
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.
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.
VAR, SVAR, vec2var,
SVEC, Phi, Psi, plot
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)
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