cointhatemij

Hatemi-J Cointegration Test with Two Unknown Regime Shifts

A Python implementation of the Hatemi-J (2008) cointegration test that allows for two structural breaks with unknown timing.

Reference

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

Features

• ✅ Three test statistics (ADF, Zt, Za)
• ✅ Endogenous detection of two structural breaks
• ✅ Multiple lag selection criteria (AIC, BIC, t-stat)
• ✅ Various variance estimation methods
• ✅ Critical values for k ≤ 4 independent variables
• ✅ Fully validated against original paper

Installation

pip install cointhatemij

Quick Start

import numpy as np
from cointhatemij import coint_hatemi_j

# Your data
y = np.array([...])  # Dependent variable
x = np.array([...])  # Independent variable(s)

# Run test
results = coint_hatemi_j(y, x)

# Check results
print(f"ADF statistic: {results['ADF_min']:.3f}")
print(f"Break dates: {results['TB1_adf']}, {results['TB2_adf']}")

Usage Example

import numpy as np
from cointhatemij import HatemiJTest

# Generate sample data
np.random.seed(123)
n = 100
x = np.random.randn(n, 2)
y = 0.5 + 0.3 * x[:, 0] + 0.2 * x[:, 1] + np.random.randn(n)

# Create test instance
test = HatemiJTest(y, x, 
                   model=3,      # Only model 3 available
                   ic=3,         # t-stat lag selection
                   pmax=8,       # Maximum 8 lags
                   varm=1,       # iid variance
                   trimm=0.10)   # 10% trimming

# Run test
results = test.fit()

# Display results
test.summary()

Parameters

• y: Dependent variable (n × 1)
• x: Independent variables (n × k), where k ≤ 4
• model: Model specification (only 3 available)
• ic: Information criterion (1=AIC, 2=BIC, 3=t-stat)
• pmax: Maximum lags for ADF test (default: 8)
• varm: Variance method (1=iid, 2=Bartlett, 3=QS)
• trimm: Trimming rate (default: 0.10)

Output

Returns dictionary with:

• ADF_min, Zt_min, Za_min: Test statistics
• TB1_adf, TB2_adf: Break dates (ADF)
• TB1_zt, TB2_zt: Break dates (Zt)
• TB1_za, TB2_za: Break dates (Za)
• cv_adf_zt, cv_za: Critical values

Critical Values

From Hatemi-J (2008), Table 1:

Methodology

The test is based on the model:

y_t = α_0 + α_1*D1_t + α_2*D2_t + β_0'*x_t + β_1'*D1_t*x_t + β_2'*D2_t*x_t + u_t

Where D1_t and D2_t are dummy variables for two structural breaks. Break dates are estimated endogenously, and three test statistics are computed as the minimum values across all possible break combinations.

Null hypothesis: No cointegration

Testing

# Run tests
pytest tests/ -v

# Run validation
python validate.py

Citation

@article{hatemi2008tests,
  title={Tests for cointegration with two unknown regime shifts},
  author={Hatemi-J, Abdulnasser},
  journal={Empirical Economics},
  volume={35},
  pages={497--505},
  year={2008}
}

@software{roudane2024cointhatemij,
  author = {Roudane, Merwan},
  title = {cointhatemij: Python implementation of Hatemi-J test},
  year = {2024},
  url = {https://github.com/merwanroudane/cointhatemij}
}

License

MIT License - see LICENSE file for details.

Author

Dr. Merwan Roudane

• Email: merwanroudane920@gmail.com
• GitHub: @merwanroudane

Support

• Issues: https://github.com/merwanroudane/cointhatemij/issues
• Documentation: https://github.com/merwanroudane/cointhatemij#readme