Chi-square test for joint hypotheses
Based on an existing bootstrap object, the test statistic allows to test joint hypotheses for selected entries of the structural matrix B. The test statistic reads as
(Rvec(\widehat{B}) - r)'R(\widehat{\mbox{Cov}}[vec(B^*)])^{-1}R'(Rvec(\widehat{b} - r)) \sim χ^2_J,
where \widehat{\mbox{Cov}}[vec(B^*)] is the estimated covariance of vectorized bootstrap estimates of structural parameters. The composite null hypothesis is H_0: Rvec(B)= r.
js.test(x, R, r = NULL)
x |
Object of class 'sboot' |
R |
A J*K^2 selection matrix, where J is the number of hypotheses and K the number of time series. |
r |
A J*1 vector of restrictions |
A list of class "jstest" with elements
test_statistic |
Test statistic |
p_value |
P-value |
R |
Selection matrix |
r |
Vector of restrictions |
Herwartz, H., 2018. 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
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)
# Bootstrapping of SVAR
bb <- wild.boot(x1, nboot = 1000, n.ahead = 30)
# Testing the hypothesis of a lower triangular matrix as
# relation between structural and reduced form errors
R <- rbind(c(0,0,0,1,0,0,0,0,0), c(0,0,0,0,0,0,1,0,0),
c(0,0,0,0,0,0,0,1,0))
c.test <- js.test(bb, R)
summary(c.test)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.