plot.westerlund_test: 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

This function provides an S3 method for visualizing objects of class westerlund_test. It creates a faceted ggplot2 visualization of the bootstrap distributions for the four Westerlund (2007) panel cointegration statistics: G_t, G_a, P_t, and 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

## S3 method for class 'westerlund_test'
plot(
  x,
  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

x	An object of class westerlund_test. This list-like object must include x$bootstrap_distributions (a numeric matrix with 4 columns for Gt, Ga, Pt, Pa) and x$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 include obs for the observed line, crit for the critical value line, fill for the density area fill, and density for the density curve outline.
lwd	A named list of line widths or sizes for the obs, crit, and density elements.
show_grid	Logical. If TRUE, displays major panel grids.
...	Additional arguments passed to or from other methods.

Details

The function converts the bootstrap distribution matrix into a long-format data frame to utilize the faceting capabilities of the ggplot2 package. This implementation uses ggplot2::geom_density() for empirical distribution estimation and arranges the four subplots into a 2x2 grid. By using facet_wrap(~Statistic, scales = "free"), the plots maintain independent x-axis scales to better visualize the specific range of each statistic. Text annotations are automatically added to each facet to display the exact numerical values of the Observed Stat and the Critical Value for quick reference.

The dashed line represents the bootstrap critical value for a left-tailed test. If the observed statistic, represented by the solid line, is located to the left of the dashed line, it indicates a rejection of the null hypothesis of no cointegration at the specified conf_level significance level. This visual approach allows for an immediate assessment of the test results relative to the empirically derived distribution.

The function requires the ggplot2, tidyr, and scales packages to be installed. Because it is an S3 method, it is typically invoked by calling plot() directly on the result object of a Westerlund test.

Value

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

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, offering a clearer picture of the distribution under the null hypothesis.

Customization

Because the function returns a ggplot object, users can modify the output easily. For example, the theme can be changed by adding a theme layer, such as plot(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: generating a mock westerlund_test object
set.seed(123)
mock_res <- 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)
)
class(mock_res) <- "westerlund_test"

## Use the S3 plot method
p <- plot(mock_res)

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

Westerlund documentation built on April 12, 2026, 5:07 p.m.