Maki Cointegration Test with Structural Breaks.

makicoint: Maki Cointegration Test with Structural Breaks

Overview

The makicoint package implements the Maki (2012) cointegration test that allows for an unknown number of structural breaks. This test is particularly useful for detecting long-run equilibrium relationships between non-stationary time series when structural changes occur over time.

Key Features

• Multiple Break Detection: Tests for cointegration with up to 5 structural breaks
• Four Model Specifications:
  • Model 0: Level shifts
  • Model 1: Level shifts with trend
  • Model 2: Regime shifts (changes in both intercept and slope)
  • Model 3: Trend and regime shifts
• Automatic Lag Selection: Uses the t-sig criterion for optimal lag determination
• Critical Values: Based on Maki (2012) Monte Carlo simulations

Installation

From CRAN (once published)

install.packages("makicoint")

Development Version from GitHub

# install.packages("devtools")
devtools::install_github("merwanroudane/makicoint")

Usage

Basic Example

library(makicoint)

# Generate cointegrated series with a structural break
set.seed(123)
n <- 100
e1 <- rnorm(n)
e2 <- rnorm(n)

# Create I(1) variables
x <- cumsum(e1)
y <- 0.5 * x + cumsum(e2)

# Add a structural break at observation 50
y[51:100] <- y[51:100] + 2

# Combine into matrix (dependent variable first)
data <- cbind(y, x)

# Run Maki test with 1 break, level shift model
result <- coint_maki(data, m = 1, model = 0)
print(result)

Testing for Two Breaks

# Generate data with two breaks
set.seed(456)
n <- 150
x2 <- cumsum(rnorm(n))
y2 <- 0.6 * x2 + cumsum(rnorm(n))

# Add two structural breaks
y2[51:100] <- y2[51:100] + 1.5
y2[101:150] <- y2[101:150] + 3

data2 <- cbind(y2, x2)

# Test with m=2
result2 <- coint_maki(data2, m = 2, model = 0)
print(result2)

Model Specifications

• model = 0: Level shift only

  • Tests for breaks in the intercept

• model = 1: Level shift with trend

  • Includes a deterministic time trend

• model = 2: Regime shift

  • Tests for breaks in both intercept and slope coefficients

• model = 3: Trend and regime shift

  • Most general model with trend and coefficient changes

Mathematical Framework

The test is based on the following cointegration regression:

Model 0 (Level Shift):

y_t = μ + Σ(μ_i * D_i,t) + β'x_t + u_t

Model 3 (Trend and Regime Shift):

y_t = μ + Σ(μ_i * D_i,t) + βt + Σ(β_i * DT_i,t) + γ'x_t + Σ(γ_i' * D_i,t * x_t) + u_t

Where D_i,t are dummy variables indicating structural breaks.

Interpretation

The test statistic is the minimum of the ADF tau statistics computed across all possible break point combinations.

• Reject the null hypothesis: Evidence of cointegration with structural breaks
• Fail to reject: No evidence of cointegration

Lower (more negative) test statistics provide stronger evidence against the null hypothesis of no cointegration.

Functions

• coint_maki(): Main function to perform the Maki cointegration test
• cv_coint_maki(): Get critical values for the test
• print.maki_test(): Print method for test results

Reference

Maki, D. (2012). Tests for cointegration allowing for an unknown number of breaks. Economic Modelling, 29(5), 2011-2015. https://doi.org/10.1016/j.econmod.2012.05.006

Author

Dr. Merwan Roudane
Independent Researcher
Email: [email protected]

License

GPL-3

Contributing

Contributions, bug reports, and feature requests are welcome! Please feel free to open an issue or submit a pull request on GitHub.