FCVARbootRank {FCVAR}

Distribution of LR Test Statistic for the Rank Test

Description

FCVARbootRank generates a distribution of a likelihood ratio test statistic for the rank test using a wild bootstrap, following the method of Cavaliere, Rahbek, and Taylor (2010). It takes the two ranks as inputs to estimate the model under the null and the model under the alternative.

Usage

FCVARbootRank(x, k, opt, r1, r2, B)

Arguments

x

A matrix of variables to be included in the system. If k>0, actual data is used for initial values.

k

The number of lags in the system.

opt

An S3 object of class FCVAR_opt that stores the chosen estimation options, generated from FCVARoptions().

r1

The cointegrating rank under the null hypothesis.

r2

The cointegrating rank under the alternative hypothesis.

B

The number of bootstrap samples.

Value

A list FCVARbootRank_stats containing the test results, including the following parameters:

LRbs

A B x 1 vector of simulated likelihood ratio statistics.

pv

An approximate p-value for the LR statistic based on the bootstrap distribution.

H

A list containing LR test results. It is identical to the output from HypoTest, with one addition, namely H$pvBS which is the bootstrap p-value)

mBS

Model estimates under the null hypothesis.

mUNR

Model estimates under the alternative hypothesis.

References

Cavaliere, G., A. Rahbek, and A. M. R. Taylor (2010). "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics 158, 7-24.

See Also

FCVARoptions to set default estimation options. HypoTest for the format of a hypothesis test results. FCVARestn for the estimates from a rectricted and unrestricted model within a hypothesis test.

Other FCVAR specification functions: FCVARlagSelect(), FCVARrankTests(), summary.FCVAR_lags(), summary.FCVAR_ranks()

Examples

opt <- FCVARoptions()
opt$gridSearch   <- 0 # Disable grid search in optimization.
opt$dbMin        <- c(0.01, 0.01) # Set lower bound for d,b.
opt$dbMax        <- c(2.00, 2.00) # Set upper bound for d,b.
opt$constrained  <- 0 # Impose restriction dbMax >= d >= b >= dbMin ? 1 <- yes, 0 <- no.
opt$plotRoots <- 0
x <- votingJNP2014[, c("lib", "ir_can", "un_can")]
set.seed(42)
FCVARbootRank_stats <- FCVARbootRank(x, k = 2, opt, r1 = 0, r2 = 1, B = 2)
# In practice, set the number of bootstraps so that (B+1)*alpha is an integer,
# where alpha is the chosen level of significance.
# For example, set B = 999 (but it takes a long time to compute).