Westerlund (version 0.1.2)

plot_westerlund_bootstrap: 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
)

Value

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

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.

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().

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.

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()