---
title: "Westerlund: Panel Cointegration Tests Based on Westerlund (2007)"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Westerlund: Panel Cointegration Tests Based on Westerlund (2007)}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

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

`Westerlund` is an R package implementing a functional approximation of the four panel cointegration tests developed by **Westerlund (2007)**. Unlike traditional residual-based tests, these statistics are based on structural dynamics. They test the null hypothesis of no cointegration by determining whether the error-correction term in a conditional error-correction model (ECM) is equal to zero.

## Key Features

The package replicates the logic of the Westerlund (2007) methodology, including:
* **Four Test Statistics**: Computes $G_t$, $G_a$, $P_t$, and $P_a$.
* **Flexible Dynamics**: Allows for unit-specific lag and lead lengths.
* **Automated Selection**: Built-in AIC selection logic for optimal lag and lead lengths.
* **Bootstrap Procedure**: Robust p-values to handle cross-sectional dependence.
* **Kernel Estimation**: Bartlett kernel long-run variance estimation.
* **Gap Handling**: Strict time-series continuity checks to ensure valid econometric results.

## Installation

You can install the development version of `Westerlund` from GitHub using the `devtools` package:

```r
# Install devtools if you haven't already
# install.packages("devtools")

# Install Westerlund
devtools::install_github("bosco-hung/Westerlund/R", build_vignettes = TRUE)

## Qucik Start
```r
library(Westerlund)

# Ensure data is sorted by ID and Time
results <- westerlund_test(
  data = my_data,
  yvar = "ln_gdp",
  xvars = c("ln_energy", "ln_capital"),
  idvar = "country",
  timevar = "year",
  constant = TRUE,
  trend = FALSE,
  lags = c(1, 3),      # AIC search between 1 and 3 lags
  leads = c(0, 2),     # AIC search between 0 and 2 leads
  bootstrap = 100,     # Run 100 bootstrap replications
  lrwindow = 3         # Bartlett kernel window size
)

# View the results table
print(results)
```

## References
Westerlund, J. (2007). Testing for Error Correction in Panel Data. Oxford Bulletin of Economics and Statistics, 69(6), 709-748.

Persyn, D., & Westerlund, J. (2008). Error-Correction-Based Cointegration Tests for Panel Data. Stata Journal, 8(2), 232-241.