Title:	Panel Cointegration Tests with Structural Breaks
Version:	1.0.4
Date:	2026-03-09
Description:	Implements panel cointegration tests allowing for structural breaks and cross-section dependence following the methodology of Banerjee and Carrion-i-Silvestre (2015) <doi:10.1002/jae.2348>. The package provides iterative factor-break estimation, individual ADF tests on defactored residuals, standardized panel test statistics, and the Bai and Ng (2004) <doi:10.1111/j.1468-0262.2004.00528.x> MQ test for identifying common stochastic trends. Supports five model specifications with varying deterministic components and break structures.
License:	GPL-3
URL:	https://github.com/muhammedalkhalaf/xtbreakcoint
BugReports:	https://github.com/muhammedalkhalaf/xtbreakcoint/issues
Encoding:	UTF-8
RoxygenNote:	7.3.2
Depends:	R (≥ 3.5.0)
Imports:	stats
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-03-09 17:54:28 UTC; acad_
Author:	Muhammad Alkhalaf [aut, cre, cph], Anindya Banerjee [ctb] (Original GAUSS code), Josep Lluis Carrion-i-Silvestre [ctb] (Original GAUSS code)
Maintainer:	Muhammad Alkhalaf <muhammedalkhalaf@gmail.com>
Repository:	CRAN
Date/Publication:	2026-03-16 16:00:03 UTC

Panel Cointegration Tests with Structural Breaks

Description

Implements panel cointegration tests allowing for structural breaks and cross-section dependence following the methodology of Banerjee and Carrion-i-Silvestre (2015). The package provides iterative factor-break estimation, individual ADF tests on defactored residuals, standardized panel test statistics, and the Bai and Ng (2004) MQ test for identifying common stochastic trends.

Details

The main function is xtbreakcoint, which performs the panel cointegration test.

Key Features:

• Accounts for cross-section dependence through common factors

• Allows for structural breaks in the cointegrating relationship

• Supports five model specifications with varying deterministic components

• Provides individual and panel test statistics

• Includes the Bai & Ng (2004) MQ test for stochastic trends

Model Specifications:

Model 1 (constant)

Constant only

Model 2 (trend)

Constant plus linear trend

Model 3 (levelshift)

Constant plus level shift at break

Model 4 (trendshift)

Constant, trend, plus level shift (default)

Model 5 (regimeshift)

Constant, trend, level shift, plus slope shift

Author(s)

Muhammad Alkhalaf

References

Banerjee, A., & Carrion-i-Silvestre, J. L. (2015). Cointegration in panel data with structural breaks and cross-section dependence. Journal of Applied Econometrics, 30(1), 1-22. doi:10.1002/jae.2348

Bai, J., & Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica, 72(4), 1127-1177. doi:10.1111/j.1468-0262.2004.00528.x

Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191-221. doi:10.1111/1468-0262.00273

Print Method for xtbreakcoint Objects

Description

Print method for objects of class "xtbreakcoint".

Usage

## S3 method for class 'xtbreakcoint'
print(x, ...)

Arguments

Value

Invisibly returns x.

See Also

xtbreakcoint, summary.xtbreakcoint

Examples

# Generate example panel data
set.seed(42)
N <- 5
T <- 30

panel_data <- data.frame(
  id = rep(1:N, each = T),
  time = rep(1:T, N),
  y = rnorm(N * T),
  x = rnorm(N * T)
)

result <- xtbreakcoint(y ~ x, data = panel_data, id = "id", time = "time",
                       max_factors = 0)
print(result)

Summary Method for xtbreakcoint Objects

Description

Summary method for objects of class "xtbreakcoint", providing detailed output including individual unit results.

Usage

## S3 method for class 'xtbreakcoint'
summary(object, ...)

Arguments

Value

Invisibly returns object.

See Also

xtbreakcoint, print.xtbreakcoint

Examples

# Generate example panel data
set.seed(42)
N <- 5
T <- 30

panel_data <- data.frame(
  id = rep(1:N, each = T),
  time = rep(1:T, N),
  y = rnorm(N * T),
  x = rnorm(N * T)
)

result <- xtbreakcoint(y ~ x, data = panel_data, id = "id", time = "time",
                       max_factors = 0)
summary(result)

Panel Cointegration Test with Structural Breaks

Description

Implements the panel cointegration test of Banerjee and Carrion-i-Silvestre (2015), allowing for structural breaks and cross-section dependence through common factors.

Usage

xtbreakcoint(
  formula,
  data,
  id,

  time,
  model = "trendshift",
  max_factors = 5,
  max_lag = 4,

  lag_method = c("auto", "fixed"),
  trim = 0.15,
  max_iter = 20,
  tolerance = 0.001
)

Arguments

Details

This function tests for panel cointegration in the presence of structural breaks and cross-sectional dependence. The methodology follows these steps:

1. Iterative Factor-Break Estimation: Jointly estimates common factors and individual break dates using an iterative procedure.

2. Individual ADF Tests: Applies ADF tests to the defactored (idiosyncratic) residuals for each cross-section unit.

3. Panel Test Statistic: Combines individual ADF statistics into a standardized panel statistic using Monte Carlo moments.

4. MQ Test: If factors are detected, tests whether they are stationary or represent stochastic trends (Bai & Ng, 2004).

Value

An object of class "xtbreakcoint" containing:

Z_t

Panel test statistic (standard normal under H0)

p_value

One-sided p-value for Z_t

tbar

Average of individual ADF t-statistics

mean_t

Expected value of t-statistic under H0

var_t

Variance of t-statistic under H0

N

Number of cross-section units

T

Number of time periods

n_factors

Number of estimated common factors

n_trends

Number of stochastic trends (from MQ test)

MQ_np

Non-parametric MQ test statistic

MQ_p

Parametric MQ test statistic

iterations

Number of iterations for factor-break convergence

reject_pct

Percentage of individual units rejecting H0 at 5%

adf_stats

Vector of individual ADF t-statistics

lag_orders

Vector of selected lag orders for each unit

breaks

Vector of estimated break dates (periods from start)

factors

Matrix of estimated common factors (T-1 x n_factors)

model

Model specification used

call

The matched call

Model Specifications

1 - constant

Constant only

2 - trend

Constant plus linear trend

3 - levelshift

Constant plus level shift at break

4 - trendshift

Constant, trend, plus level shift (default)

5 - regimeshift

Constant, trend, level shift, plus slope shift

Author(s)

Muhammad Alkhalaf

References

Banerjee, A., & Carrion-i-Silvestre, J. L. (2015). Cointegration in panel data with structural breaks and cross-section dependence. Journal of Applied Econometrics, 30(1), 1-22. doi:10.1002/jae.2348

Bai, J., & Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica, 72(4), 1127-1177. doi:10.1111/j.1468-0262.2004.00528.x

Examples

# Generate example panel data
set.seed(42)
N <- 10  # panels
T <- 50  # time periods

# Create cointegrated data with a structural break
panel_data <- data.frame(
  id = rep(1:N, each = T),
  time = rep(1:T, N),
  y = NA,
  x = NA
)

for (i in 1:N) {
  idx <- panel_data$id == i
  x <- cumsum(rnorm(T))
  u <- rnorm(T, sd = 0.5)
  # Cointegrating relationship with break at t=25
  beta <- ifelse(1:T <= 25, 1, 1.5)
  y <- 1 + beta * x + u
  panel_data$x[idx] <- x
  panel_data$y[idx] <- y
}

# Test for cointegration
result <- xtbreakcoint(y ~ x, data = panel_data, id = "id", time = "time")
print(result)