segmcoint 1.0.0

Tests for Segmented Cointegration: Kim (2003) and Martins & Rodrigues (2022)

segmcoint

Tests for Segmented Cointegration

A Python library implementing rigorous tests for segmented cointegration from two seminal econometric papers:

1. Kim, J.-Y. (2003). Inference on Segmented Cointegration. Econometric Theory, 19, 620–639.
2. Martins, L.F. and Rodrigues, P.M.M. (2022). Tests for Segmented Cointegration: An Application to US Governments Budgets. Empirical Economics, 63, 567–600.

Overview

Cointegration relations are often interpreted as long-run equilibrium relationships. In practice, however, real data frequently fail to confirm cointegration for well-understood economic relations. This package addresses the possibility that failure to confirm cointegration is due to nonstationary deviations in a relatively small portion of the data ("short-run"), while the cointegration relation prevails in the remaining periods—a situation called segmented cointegration.

Kim (2003) Tests

• Phillips–Perron–Ouliaris type tests: $Z^_\rho(\mathcal{C})$ and $Z^_t(\mathcal{C})$
• Augmented Dickey–Fuller type tests: $ADF^_\rho(\mathcal{C})$ and $ADF^_t(\mathcal{C})$
• Extremum estimator for break date identification (Eq. 3.16–3.17)
• Critical values from Tables 1 and 2 of the paper (for $\bar{\ell}(\mathcal{T}_N) = 0.3$)

Martins & Rodrigues (2022) Tests

• Wald-type statistics: $F_A(\tau, m^)$ and $F_B(\tau, m^)$ (Eq. 3.2)
• Supremum statistics: $\sup F_A(m^)$ and $\sup F_B(m^)$ (Eq. 3.3)
• Combined test: $W(m^*)$ (Eq. 3.4)
• Double maximum test: $W_{\max}$ (Eq. 3.5)
• Critical values from Table 1 of the paper
• Break date estimation (Remark 3)

Installation

pip install .

Or for development:

pip install -e ".[dev]"

Quick Start

import numpy as np
from segmcoint import kim_test, mr_test, generate_segmented_data

# Generate data with segmented cointegration
y, X, eps, info = generate_segmented_data(T=200, rho=0.85, seed=42)

# Kim (2003) tests
res_kim = kim_test(y, X, model='drift')
print(res_kim)

# Martins & Rodrigues (2022) tests
res_mr = mr_test(y, X, model='drift')
print(res_mr)

Model Specifications

Three deterministic specifications are supported, following Kim (2003, Eq. 2.1a–2.1c):

Model	Equation	Kim (2003)	M&R (2022)
'none'	$x_{1t} = \beta' x_{2t} + \varepsilon_t$	Case I	No det.
'drift'	$x_{1t} = \alpha + \beta' x_{2t} + \varepsilon_t$	Case II	Intercept
'trend'	$x_{1t} = \alpha + \gamma t + \beta' x_{2t} + \varepsilon_t$	Case III	Int.+Trend

API Reference

kim_test(y, X, model, max_ell, step, ...)

Computes the infimum test statistics from Kim (2003). Returns a KimTestResult object.

mr_test(y, X, model, max_breaks, epsilon, step, ...)

Computes the Wald-type test statistics from Martins & Rodrigues (2022). Returns an MRTestResult object.

kim_break_estimator(y, X, model, max_ell, step)

Extremum estimator for the noncointegration period (Kim 2003, Eq. 3.16–3.17).

generate_segmented_data(T, beta, rho, ...)

Generate simulated data from a segmented cointegration DGP.

Testing

pytest tests/ -v

Author

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

License

MIT License

References

• Kim, J.-Y. (2003). Inference on Segmented Cointegration. Econometric Theory, 19, 620–639.
• Martins, L.F. and Rodrigues, P.M.M. (2022). Tests for Segmented Cointegration: An Application to US Governments Budgets. Empirical Economics, 63, 567–600.
• Phillips, P.C.B. and Ouliaris, S. (1990). Asymptotic Properties of Residual Based Tests for Cointegration. Econometrica, 58, 165–193.
• Kejriwal, M., Perron, P., and Zhou, J. (2013). Wald Tests for Detecting Multiple Structural Changes in Persistence. Econometric Theory, 29, 289–323.