cointsmall

Overview

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

Installation

# Install from CRAN (when available)
install.packages("cointsmall")

# Or install the development version from GitHub

Features

Small sample focused: Critical values adjusted for small samples using response surface methodology
Structural breaks: Test for cointegration allowing for 0, 1, or 2 structural breaks
Multiple model specifications:
- Model “o”: No structural break
- Model “c”: Break in constant (level shift)
- Model “cs”: Break in constant and slope (regime change)
Endogenous break detection: Break dates determined by minimizing ADF statistic or SSR
Combined testing: Evaluate all models simultaneously with automatic model selection

Usage

Basic Cointegration Test

library(cointsmall)

# 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 structural break
result <- cointsmall(y, x, breaks = 0)
print(result)

Testing with Structural Breaks

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

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

Combined Testing Procedure

# Test all model specifications
combined <- cointsmall_combined(y_break, x, breaks = 1)
print(combined)

Critical Values

# Get critical values for specific parameters
cv <- cointsmall_cv(T = 50, m = 1, breaks = 1, model = "cs")
print(cv)

Models

Model	Description	Cointegrating Regression
o	No break	y = α + β’x + ε
c	Break in constant	y = α₁ + α₂D + β’x + ε
cs	Break in constant and slope	y = α₁ + α₂D + β₁’x + β₂’(x·D) + ε

Where D is a dummy variable equal to 1 after the break date.

References

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

Author

License

GPL (>= 3)