Wild bootstrap for IRFs of identified SVARs
Calculating confidence bands for impulse response functions via wild bootstrap techniques (Goncalves and Kilian, 2004).
wild.boot( x, design = "fixed", distr = "rademacher", n.ahead = 20, nboot = 500, nc = 1, dd = NULL, signrest = NULL, signcheck = TRUE, itermax = 300, steptol = 200, iter2 = 50, rademacher = "deprecated" )
x |
SVAR object of class "svars" |
design |
character. If design="fixed", a fixed design bootstrap is performed. If design="recursive", a recursive design bootstrap is performed. |
distr |
character. If distr="rademacher", the Rademacher distribution is used to generate the bootstrap samples. If distr="mammen", the Mammen distribution is used. If distr = "gaussian", the gaussian distribution is used. |
n.ahead |
Integer specifying the steps |
nboot |
Integer. Number of bootstrap iterations |
nc |
Integer. Number of processor cores |
dd |
Object of class 'indepTestDist'. A simulated independent sample of the same size as the data. roxIf not supplied, it will be calculated by the function |
signrest |
A list with vectors containing 1 and -1, e.g. c(1,-1,1), indicating a sign pattern of specific shocks to be tested with the help of the bootstrap samples. |
signcheck |
Boolean. Whether the sign pattern should be checked for each bootstrap iteration. Note that this procedure is computationally extremely demanding for high dimensional VARs, since the number of possible permutations of B is K!, where K is the number of variables in the VAR. |
itermax |
Integer. Maximum number of iterations for DEoptim |
steptol |
Integer. Tolerance for steps without improvement for DEoptim |
iter2 |
Integer. Number of iterations for the second optimization |
rademacher |
deprecated, use "design" instead. |
A list of class "sboot" with elements
true |
Point estimate of impulse response functions |
bootstrap |
List of length "nboot" holding bootstrap impulse response functions |
SE |
Bootstrapped standard errors of estimated covariance decomposition (only if "x" has method "Cramer von-Mises", or "Distance covariances") |
nboot |
Number of bootstrap iterations |
distr |
Character, whether the Gaussian, Rademacher or Mammen distribution is used in the bootstrap |
design |
character. Whether a fixed design or recursive design bootstrap is performed |
point_estimate |
Point estimate of covariance decomposition |
boot_mean |
Mean of bootstrapped covariance decompositions |
signrest |
Evaluated sign pattern |
sign_complete |
Frequency of appearance of the complete sign pattern in all bootstrapped covariance decompositions |
sign_part |
Frequency of bootstrapped covariance decompositions which conform the complete predetermined sign pattern. If signrest=NULL, the frequency of bootstrapped covariance decompositions that hold the same sign pattern as the point estimate is provided. |
sign_part |
Frequency of single shocks in all bootstrapped covariance decompositions which accord to a specific predetermined sign pattern |
cov_bs |
Covariance matrix of bootstrapped parameter in impact relations matrix |
method |
Used bootstrap method |
VAR |
Estimated input VAR object |
Goncalves, S., Kilian, L., 2004. Bootstrapping autoregressions with conditional heteroskedasticity of unknown form. Journal of Econometrics 123, 89-120.
Herwartz, H., 2017. Hodges Lehmann detection of structural shocks -
An analysis of macroeconomic dynamics in the Euro Area, Oxford Bulletin of Economics and Statistics
# data contains quarterly observations from 1965Q1 to 2008Q3 # x = output gap # pi = inflation # i = interest rates set.seed(23211) v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" ) x1 <- id.dc(v1) summary(x1) # impulse response analysis with confidence bands # Checking how often theory based impact relations appear signrest <- list(demand = c(1,1,1), supply = c(-1,1,1), money = c(-1,-1,1)) bb <- wild.boot(x1, nboot = 500, n.ahead = 30, nc = 1, signrest = signrest) summary(bb) # Plotting IRFs with confidance bands plot(bb, lowerq = 0.16, upperq = 0.84) # With different confidence levels plot(bb, lowerq = c(0.05, 0.1, 0.16), upperq = c(0.95, 0.9, 0.84)) # Halls percentile plot(bb, lowerq = 0.16, upperq = 0.84, percentile = 'hall') # Bonferroni bands plot(bb, lowerq = 0.16, upperq = 0.84, percentile = 'bonferroni')
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