quantilecoint 1.0.0

Quantile Cointegrating Regression - Implementation based on Xiao (2009) Journal of Econometrics

Quantilecoint

Quantile Cointegrating Regression - A Python implementation based on Xiao (2009) "Quantile cointegrating regression", Journal of Econometrics, 150, 248-260.

Author

Dr Merwan Roudane
Email: [e-mail]
GitHub: https://github.com/merwanroudane/quantilecoint

Overview

This package implements quantile regression methods for cointegrated time series, including:

• Quantile Cointegrating Regression: Estimate cointegrating relationships at different quantiles
• Fully-Modified Quantile Regression: Bias-corrected estimator for endogenous regressors
• Augmented Quantile Cointegrating Regression: Uses leads and lags to handle endogeneity
• Wald Test: Test linear restrictions on cointegrating coefficients
• Stability Test: Bootstrap-based test for constant vs. time-varying coefficients
• CUSUM Cointegration Test: Robust test for the null of cointegration

Installation

pip install quantilecoint

Or install from source:

git clone https://github.com/merwanroudane/quantilecoint.git
cd quantilecoint
pip install -e .

Quick Start

import numpy as np
from quantilecoint import QuantileCointegration

# Generate sample data
np.random.seed(42)
n = 200
x = np.cumsum(np.random.randn(n))  # I(1) process
y = 2.0 + 1.5 * x + np.random.randn(n)  # Cointegrated with x

# Fit quantile cointegrating regression
model = QuantileCointegration(y, x, n_lags=4)

# Estimate at different quantiles
results = model.fit(quantiles=[0.1, 0.25, 0.5, 0.75, 0.9])

# Print publication-ready results
print(results.summary())

# Test for constant coefficients
stability_test = model.test_stability()
print(stability_test)

Main Features

1. Quantile Cointegrating Regression

from quantilecoint import QuantileCointegration

model = QuantileCointegration(y, x, n_lags=4)
results = model.fit(tau=0.5)  # Median regression

# Get fully-modified estimates (bias-corrected)
fm_results = model.fit_fully_modified(tau=0.5)

2. Test for Time-Varying Coefficients

# Test H0: β(τ) = β (constant across quantiles)
stability = model.test_stability(
    quantiles=np.arange(0.05, 0.96, 0.05),
    n_bootstrap=1000
)
print(f"Test statistic: {stability.statistic:.4f}")
print(f"Critical values (1%, 5%, 10%): {stability.critical_values}")

3. Wald Test for Restrictions

# Test H0: β = 1
wald = model.wald_test(R=np.array([[0, 1]]), r=np.array([1]), tau=0.5)
print(f"Wald statistic: {wald.statistic:.4f}")
print(f"P-value: {wald.pvalue:.4f}")

4. CUSUM Cointegration Test

# Test null of cointegration
cusum = model.test_cointegration(tau=0.5)
print(f"CUSUM statistic: {cusum.statistic:.4f}")

Output Format

Results are formatted for publication in top journals:

==============================================================================
                    Quantile Cointegrating Regression Results
==============================================================================
Dep. Variable:                      y   No. Observations:                  200
Method:              Quantile Regression (Fully-Modified)
Date:                Mon, 20 Jan 2026   Number of Lags:                      4
Time:                        02:43:00   
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          2.0134      0.089     22.623      0.000       1.839       2.188
x              1.4987      0.012    124.892      0.000       1.475       1.522
==============================================================================

Quantile Coefficient Estimates:
------------------------------------------------------------------------------
   τ     β(τ)    Std.Err   95% CI Lower   95% CI Upper
------------------------------------------------------------------------------
  0.10   1.423    0.018       1.388          1.458
  0.25   1.467    0.014       1.440          1.494
  0.50   1.499    0.012       1.475          1.522
  0.75   1.531    0.014       1.504          1.558
  0.90   1.576    0.019       1.539          1.613
------------------------------------------------------------------------------

References

• Xiao, Z. (2009). Quantile cointegrating regression. Journal of Econometrics, 150(2), 248-260.
• Koenker, R., & Bassett, G. (1978). Regression quantiles. Econometrica, 46(1), 33-50.
• Koenker, R., & Xiao, Z. (2006). Quantile autoregression. Journal of the American Statistical Association, 101(475), 980-990.

License

MIT License - see LICENSE file for details.

Citation

If you use this package in your research, please cite:

@software{roudane2026quantilecoint,
  author = {Roudane, Merwan},
  title = {quantilecoint: Quantile Cointegrating Regression in Python},
  year = {2026},
  url = {https://github.com/merwanroudane/quantilecoint}
}

And the original paper:

@article{xiao2009quantile,
  title={Quantile cointegrating regression},
  author={Xiao, Zhijie},
  journal={Journal of Econometrics},
  volume={150},
  number={2},
  pages={248--260},
  year={2009},
  publisher={Elsevier}
}