mb.boot: Moving block bootstrap for IRFs of identified SVARs

Description

Calculating confidence bands for impulse response via moving block bootstrap

Usage

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
)

Value

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

Arguments

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

References

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.

Examples

Run this code

# \donttest{
# 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')
# }