boostvar: An R package for computing the p-values in high-dimensional vector autoregression

This R package computes the least-squares boosting estimates, standard errors, and p-values for vector autoregression models.

This package also offers a function boostls.R to compute the estimates, standard errors, and p-values for a cross-section regression.

Installation

You can install boostvar from GitHub with:

devtools::install_github("xhuang20/boostvar")

An example of vector autoregression

We give an example for a bivariate VAR model.

library(boostvar)
# An example of bivariate vector autoregression
set.seed(123)
p = 2
d = 2
nobs = 100
bstop = 50
y = matrix(0, nobs, d)
b0 = matrix(c(0.02,0.03),2,1)
b1 = matrix(c(0.5,0.4,0.1,0.5),2,2)
b2 = matrix(c(0,0.25,0,0),2,2)
for (i in (p+1):dim(y)[1]) {
      y[i,] = t(b0) + t(b1 %*%  y[i-1,]) + t(b2 %*% y[i-2,]) +
      c(rnorm(1,0,0.3), rnorm(1,0,0.2))
}
y = tail(y,-p)
result = boostvar(y, p = p, bstop = bstop, nu = 0.1, group.type = 1)
dim(result$beta)
#> [1]  2  2  2 50
dim(result$pval)
#> [1]  2  2  2 50

The object result includes all LS-Boost estimates at each of the 50 steps and their p-values. The component result$beta is a 4-dimensional array, where the 3rd dimension corresponds to each of the lag in a VAR and the 4th dimension corresponds to each boosting step. Dimensions 1 and 2 are the same as the number of variables in a VAR so that, for example, result$beta[,,2,3] is the estimated square coefficient matrix for the 2nd lag at boosting step 3. Values in the component result$se are the standard errors that can be used to construct confidence intervals.

An example of cross-section regression

We use the red wine quality data from [https://archive.ics.uci.edu/ml/datasets/wine+Quality] as an example in cross-section regression.

data.link = "https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-red.csv"
redwine = read.csv(data.link, header = TRUE, sep = ';')
redwine = redwine[1:100,]   # Try the first 100 observations.
result = boostls(y = redwine$quality,
                 x = subset(redwine, select = -c(quality)),
                 bstop = 50,
                 nu = 0.1)
dim(result$beta)
#> [1] 11 50
dim(result$pval)
#> [1] 11 50

The component result$beta stores the boosting estimates for 11 regressors in 50 steps. The component result$pval gives p-values for all nonzero estimates in result$beta. Again, the standard errors in result$se can be used to compute the confidence intervals.

References

Huang, X. (2022) Boosted p-values for high-dimensional vector autoregression, working paper.