plot_westerlund_bootstrap: Plot Bootstrap Distributions for Westerlund ECM Panel...

In Westerlund: Panel Cointegration Tests Based on Westerlund (2007)

Plot Bootstrap Distributions for Westerlund ECM Panel Cointegration Tests

Description

Creates a faceted ggplot2 visualization of the bootstrap distributions for the four Westerlund (2007) panel cointegration statistics (G_t, G_a, P_t, P_a). The plot displays the kernel density of bootstrap replications, the observed test statistic as a solid line, and the left-tail bootstrap critical value as a dashed line.

Usage

plot_westerlund_bootstrap(
  results,
  title = "Westerlund Test: Bootstrap Distributions",
  conf_level = 0.05,
  colors = list(
    obs = "#D55E00",
    crit = "#0072B2",
    fill = "grey80",
    density = "grey30"
  ),
  lwd = list(obs = 1, crit = 0.8, density = 0.5),
  show_grid = TRUE
)

Arguments

results	A list-like object containing bootstrap output. It must include: results$bootstrap_distributions (a numeric matrix with 4 columns for Gt, Ga, Pt, Pa) and results$test_stats (a named list or vector containing the observed statistics).
title	Character. The main title of the plot.
conf_level	Numeric in (0,1). Left-tail quantile used as the critical value. For example, conf_level = 0.05 identifies the 5% left-tail critical value.
colors	A named list of colors for plot elements. Expected elements: obs (observed line), crit (critical value line), fill (density area fill), and density (density curve outline).
lwd	A named list of line widths (or sizes) for obs, crit, and density.
show_grid	Logical. If TRUE, displays major panel grids.

Details

Implementation Details. The function converts the bootstrap distribution matrix into a long-format data frame to utilize ggplot2::facet_wrap().

Unlike the base R version, this implementation:

• Uses ggplot2::geom_density() for empirical distribution estimation.

• Arranges the four subplots into a 2x2 grid with independent x-axis scales using facet_wrap(~Statistic, scales = "free").

• Adds text annotations to each facet displaying the exact numerical values of the Observed Stat and the Critical Value.

Interpretation. The dashed line represents the bootstrap critical value for a left-tailed test. If the observed statistic (solid line) is to the left of the dashed line, it indicates a rejection of the null hypothesis (H_0: no cointegration) at the conf_level significance level.

Dependencies. The function requires the ggplot2, tidyr, and scales packages.

Value

Returns a ggplot object. This allows the user to apply further customizations, such as changing themes (+ theme_bw()) or adding additional layers.

Inference and Visualization

Why use bootstrap distributions?

Westerlund's pooled statistics can be sensitive to nuisance parameters and cross-sectional dependence in finite samples. Visualizing the bootstrap density provides a more robust reference than asymptotic normal curves.

Customization

Because the function returns a ggplot object, users can modify the output easily. For example, to change the theme: plot_westerlund_bootstrap(res) + ggplot2::theme_dark().

References

Westerlund, J. (2007). Testing for error correction in panel data. Oxford Bulletin of Economics and Statistics, 69(6), 709–748.

See Also

westerlund_test, WesterlundBootstrap, DisplayWesterlund

Examples

## Example: minimal mock results object
set.seed(123)
mock <- list(
  bootstrap_distributions = cbind(
    Gt = rnorm(399, mean = -2, sd = 1),
    Ga = rnorm(399, mean = -8, sd = 3),
    Pt = rnorm(399, mean = -2, sd = 1),
    Pa = rnorm(399, mean = -6, sd = 3)
  ),
  test_stats = list(Gt = -3.1, Ga = -10.2, Pt = -2.7, Pa = -7.8)
)

## Generate the faceted ggplot
p <- plot_westerlund_bootstrap(mock)

## Display plot
if (interactive()) print(p)

## Add ggplot2 layers
# p + ggplot2::theme_classic()

Westerlund documentation built on Feb. 7, 2026, 5:07 p.m.