Type:	Package
Title:	Cointegration Tests with Structural Breaks in Small Samples
Version:	1.0.2
Description:	Implements cointegration tests with structural breaks designed for small sample sizes, following the methodology of Trinh (2022) https://ideas.repec.org/p/ema/worpap/2022-01.html. Supports models with no breaks, breaks in constant only, and breaks in both constant and slope. Provides endogenous break date detection using ADF or SSR minimization criteria, with small-sample adjusted critical values via response surface methodology.
License:	GPL-3
URL:	https://github.com/muhammedalkhalaf/cointsmall
BugReports:	https://github.com/muhammedalkhalaf/cointsmall/issues
Encoding:	UTF-8
Depends:	R (≥ 3.5.0)
Imports:	stats
Suggests:	testthat (≥ 3.0.0)
RoxygenNote:	7.3.1
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-03-13 20:45:25 UTC; acad_
Author:	Muhammad Alkhalaf [aut, cre, cph], Hoang Huy Trinh [ctb]
Maintainer:	Muhammad Alkhalaf <muhammedalkhalaf@gmail.com>
Repository:	CRAN
Date/Publication:	2026-03-19 14:00:02 UTC

cointsmall: Cointegration Tests with Structural Breaks in Small Samples

Description

The cointsmall package implements cointegration tests designed for small sample sizes with potential structural breaks. It follows the methodology of Trinh (2022), which provides small-sample adjusted critical values for testing the null hypothesis of no cointegration.

Main Functions

cointsmall

Main function to perform cointegration tests with optional structural breaks

cointsmall_combined

Combined testing procedure that evaluates all model specifications

cointsmall_cv

Retrieve critical values for different model specifications

Models

Three model specifications are supported:

Model "o"

No structural break - standard cointegration test

Model "c"

Break in constant only - shift in intercept at break date

Model "cs"

Break in constant and slope - shift in both intercept and cointegrating coefficients

Author(s)

Maintainer:

Other contributors:

• Hoang Huy Trinh (Author of the underlying methodology) [contributor]

References

Trinh, H. H. (2022). Testing for cointegration with structural changes in very small sample. THEMA Working Paper n°2022-01, CY Cergy Paris Université. https://ideas.repec.org/p/ema/worpap/2022-01.html

Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99-126. doi:10.1016/0304-4076(69)41685-7

Hatemi-J, A. (2008). Tests for cointegration with two unknown regime shifts with an application to financial market integration. Empirical Economics, 35(3), 497-505. doi:10.1007/s00181-007-0175-9

Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251-276. doi:10.2307/1913236

Cointegration Test with Structural Breaks in Small Samples

Description

Tests for cointegration between a dependent variable and one or more independent variables, allowing for structural breaks. The method is designed specifically for small sample sizes following Trinh (2022).

Usage

cointsmall(
  y,
  x,
  breaks = 1,
  model = NULL,
  criterion = "adf",
  trim = 0.15,
  maxlags = -1,
  level = 5
)

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

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

Arguments

Details

The test follows the two-step Engle-Granger procedure with modifications for structural breaks:

1. Estimate the cointegrating regression (with break dummies if applicable)

2. Apply an ADF test to the residuals

For models with breaks, the break date(s) are determined endogenously by searching over all possible dates within the trimmed sample and selecting the date that minimizes the ADF statistic or SSR.

Critical values are computed using response surface methodology following Trinh (2022), which accounts for the small sample bias.

Value

An object of class "cointsmall" containing:

References

Trinh, H. H. (2022). Testing for cointegration with structural changes in very small sample. THEMA Working Paper n°2022-01, CY Cergy Paris Université. https://ideas.repec.org/p/ema/worpap/2022-01.html

Examples

# Generate cointegrated series
set.seed(42)
n <- 50
e <- cumsum(rnorm(n))  # Common stochastic trend
y <- 2 + 3 * e + rnorm(n, sd = 0.5)
x <- e + rnorm(n, sd = 0.3)

# Test with no break
result0 <- cointsmall(y, x, breaks = 0)
print(result0)

# Test with one break (break in constant and slope)
result1 <- cointsmall(y, x, breaks = 1, model = "cs")
print(result1)

# Generate series with structural break
y_break <- c(2 + 2 * e[1:25], 5 + 4 * e[26:50]) + rnorm(n, sd = 0.3)
result_break <- cointsmall(y_break, x, breaks = 1)
print(result_break)

Combined Cointegration Testing Procedure

Description

Performs cointegration tests under all model specifications (no break, break in constant, break in constant and slope) and provides model selection guidance.

Usage

cointsmall_combined(y, x, breaks = 1, trim = 0.15, maxlags = -1, level = 5)

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

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

Arguments

Details

The combined procedure tests three model specifications:

1. Model "o": No structural break

2. Model "c": Break in constant only

3. Model "cs": Break in constant and slope

Model selection follows these rules:

• If no model rejects H0: No evidence of cointegration

• If exactly one model rejects H0: Select that model

• If multiple models reject H0: Select the most general model that rejects H0 (cs > c > o)

Value

An object of class "cointsmall_combined" containing:

References

Trinh, H. H. (2022). Testing for cointegration with structural changes in very small sample. THEMA Working Paper n°2022-01, CY Cergy Paris Université. https://ideas.repec.org/p/ema/worpap/2022-01.html

Examples

# Generate cointegrated series with break
set.seed(123)
n <- 50
e <- cumsum(rnorm(n))
x <- e + rnorm(n, sd = 0.3)
y <- c(2 + 2 * e[1:25], 5 + 4 * e[26:50]) + rnorm(n, sd = 0.3)

# Combined test
result <- cointsmall_combined(y, x, breaks = 1)
print(result)

Critical Values for Cointegration Tests with Structural Breaks

Description

Computes critical values for the small-sample cointegration test using response surface methodology following Trinh (2022).

Usage

cointsmall_cv(TT, m, breaks = 0, model = "o", level = NULL)

Arguments

Details

Critical values are computed using response surface equations that account for:

• Small sample sizes (TT)

• Number of regressors (m)

• Number of structural breaks

• Model specification (level shift vs. regime shift)

The response surface follows the general form:

cv = c_\infty + c_1/TT + c_2/TT^2

where the coefficients depend on m, breaks, and model.

For model "o" (no breaks), critical values are based on Engle-Granger (1987) and MacKinnon (1991, 2010) response surfaces.

For models with breaks, critical values incorporate adjustments from Gregory-Hansen (1996), Hatemi-J (2008), and small-sample corrections from Trinh (2022).

Value

If level is specified, returns the critical value. If NULL, returns a named list with cv01, cv05, and cv10.

References

Trinh, H. H. (2022). Testing for cointegration with structural changes in very small sample. THEMA Working Paper n°2022-01, CY Cergy Paris Université. https://ideas.repec.org/p/ema/worpap/2022-01.html

MacKinnon, J. G. (2010). Critical values for cointegration tests. Queen's Economics Department Working Paper No. 1227. doi:10.22004/ag.econ.279422

Examples

# Critical values for m=1 regressor, TT=30, no breaks
cointsmall_cv(TT = 30, m = 1, breaks = 0, model = "o")

# Critical values with one break (model cs)
cointsmall_cv(TT = 50, m = 2, breaks = 1, model = "cs")