Moving block bootstrap for IRFs of identified SVARs
Calculating confidence bands for impulse response via moving block bootstrap
mb.boot( x, design = "recursive", b.length = 15, n.ahead = 20, nboot = 500, nc = 1, dd = NULL, signrest = NULL, signcheck = TRUE, itermax = 300, steptol = 200, iter2 = 50 )
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. |
b.length |
Integer. Length of each block |
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. If 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 |
Numeric. Tolerance for steps without improvement for DEoptim |
iter2 |
Integer. Number of iterations for the second optimization |
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 |
design |
character. Whether a fixed design or recursive design bootstrap is performed |
b_length |
Length of each block |
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 |
Brueggemann, R., Jentsch, C., and Trenkler, C., 2016. Inference in VARs with conditional heteroskedasticity of unknown form. Journal of Econometrics 191, 69-85.
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 <- mb.boot(x1, b.length = 15, 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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