MTNARDL: Multiple Threshold Nonlinear ARDL

Author: Dr. Merwan Roudane

A comprehensive Python library for estimating Multiple Threshold Nonlinear Autoregressive Distributed Lag (MTNARDL) models with support for arbitrary number of regimes.

📚 Overview

MTNARDL extends the standard NARDL framework by:

• Multiple quantile-based thresholds (not just positive/negative)
• Endogenous threshold detection via grid search (minimizing RSS)
• Any number of regimes (2, 3, 5, 10, or custom quantiles)
• Complete statistical testing suite

🔬 Methodology

Based on the following econometric papers:

• Cho, Greenwood-Nimmo, and Shin (2020c): "Testing for the Threshold Autoregressive Distributed Lag Model"
• Cho, Greenwood-Nimmo, and Shin (2020d): "The Threshold Autoregressive Distributed Lag Model"
• Shin, Yu, and Greenwood-Nimmo (2014): Festschrift in Honor of Peter Schmidt
• Pal and Mitra (2015): Economic Modelling, 51, 436-443
• Pesaran, Shin, and Smith (2001): Journal of Applied Econometrics

📦 Installation

pip install mtnardl

Or install from source:

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

Dependencies

numpy>=1.20.0
pandas>=1.3.0
scipy>=1.7.0
statsmodels>=0.13.0
matplotlib>=3.4.0
tabulate>=0.8.9
openpyxl>=3.0.0

🚀 Quick Start

Basic 3-Regime TNARDL (like Stata tnardl)

import mtnardl as mt
import pandas as pd

# Load your data
data = pd.read_csv('oil_prices.csv', parse_dates=['date'])
data.set_index('date', inplace=True)

# Estimate 3-regime TNARDL model
model = mt.MTNARDL(
    data=data,
    depvar='gasoline',
    threshold_var='crude_oil',
    control_vars=['volume'],
    n_regimes=3,
    max_lags=4,
    criterion='aic'
)

# Fit the model
model.fit(verbose=True)

# Print results
print(model.summary())

5-Regime Quintile MTNARDL (Pal & Mitra 2015)

model5 = mt.MTNARDL(
    data=data,
    depvar='gasoline',
    threshold_var='crude_oil',
    n_regimes=5,
    threshold_method='quantile'
)
model5.fit()

10-Regime Decile MTNARDL

model10 = mt.MTNARDL(
    data=data,
    depvar='gasoline',
    threshold_var='crude_oil',
    n_regimes=10,
    threshold_method='quantile'
)
model10.fit()

Custom Quantiles

model_custom = mt.MTNARDL(
    data=data,
    depvar='gasoline',
    threshold_var='crude_oil',
    quantiles=[0.25, 0.5, 0.75],  # Creates 4 regimes
    threshold_method='quantile'
)
model_custom.fit()

📊 Statistical Tests

Bounds Test for Cointegration

from mtnardl.tests import BoundsTest

bt = BoundsTest(model)
result = bt.test(case='case3')
print(bt.summary())

Asymmetry Tests (Long-run, Short-run, Joint)

from mtnardl.tests import AsymmetryTests

at = AsymmetryTests(model)
asym_results = at.test()
print(at.summary())

Diagnostic Tests

from mtnardl.tests import DiagnosticTests

dt = DiagnosticTests(model)
diag_results = dt.test()
print(dt.summary())

QLR Test for Structural Breaks

from mtnardl.tests import QLRTest

qlr = QLRTest(model)
result = qlr.test(trim=0.15)
print(qlr.summary())

# Plot F-statistics over potential break dates
qlr.plot()

📈 Visualization

Dynamic Multiplier Plots

from mtnardl.visualization import plot_dynamic_multipliers

fig = plot_dynamic_multipliers(model, horizon=20)
fig.savefig('multipliers.png', dpi=300)

Stability Analysis (CUSUM/CUSUMQ)

from mtnardl.visualization import plot_cusum, plot_cusumq, plot_stability

# Individual plots
plot_cusum(model, save_path='cusum.png')
plot_cusumq(model, save_path='cusumq.png')

# Combined plot
plot_stability(model, save_path='stability.png')

📋 Export Results

Excel

from mtnardl.output import to_excel

to_excel(model, 'results.xlsx',
         asymmetry_results=asym_results,
         diagnostics=diag_results,
         bounds_result=result)

LaTeX

from mtnardl.output import to_latex

to_latex(model, 'results.tex', style='booktabs')

HTML Report

from mtnardl.output import to_html

to_html(model, 'report.html', style='modern')

🔧 API Reference

MTNARDL Class

MTNARDL(
    data,                    # pd.DataFrame: Input data
    depvar,                  # str: Dependent variable name
    threshold_var,           # str: Variable for threshold decomposition
    control_vars=None,       # list: Additional control variables
    max_lags=4,             # int: Maximum lags for ARDL
    criterion='aic',        # str: Lag selection criterion
    n_regimes=3,            # int: Number of regimes
    trim=0.15,              # float: Trimming for grid search
    threshold_method='grid_search',  # str: 'grid_search' or 'quantile'
    quantiles=None,         # list: Custom quantile positions
    ec=True                 # bool: Error correction form
)

Key Properties

• model.thresholds_ - Detected threshold values
• model.partial_sums_ - Decomposed partial sum series
• model.results - Complete estimation results

Result Attributes

• results.coefficients - Estimated coefficients
• results.std_errors - Standard errors
• results.t_stats - T-statistics
• results.p_values - P-values
• results.long_run - Long-run multipliers
• results.ec_term - Error correction term
• results.r_squared - R-squared
• results.aic, results.bic - Information criteria

📖 Examples

See the examples/ directory for complete notebooks:

• 01_basic_usage.ipynb - Getting started
• 02_oil_prices.ipynb - Replicating Pal & Mitra (2015)
• 03_exchange_rates.ipynb - Exchange rate asymmetry
• 04_custom_thresholds.ipynb - Custom configurations

📜 Citation

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

@software{roudane2026mtnardl,
  author = {Roudane, Merwan},
  title = {MTNARDL: Multiple Threshold Nonlinear ARDL for Python},
  year = {2026},
  url = {https://github.com/merwanroudane/mtnardl}
}

📚 References

1. Cho, J., Greenwood-Nimmo, M., & Shin, Y. (2020c). Testing for the Threshold Autoregressive Distributed Lag Model. Mimeo: University of York.

2. Cho, J., Greenwood-Nimmo, M., & Shin, Y. (2020d). The Threshold Autoregressive Distributed Lag Model. Mimeo: University of York.

3. Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling Asymmetric Cointegration and Dynamic Multipliers in a Nonlinear ARDL Framework. Festschrift in Honor of Peter Schmidt, 281-314.

4. Pal, D., & Mitra, S.K. (2015). Asymmetric impact of crude price on oil product pricing in the United States. Economic Modelling, 51, 436-443.

5. Pesaran, M.H., Shin, Y., & Smith, R.J. (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16(3), 289-326.

📄 License

MIT License - see LICENSE file.

👤 Contact

Dr. Merwan Roudane

• GitHub: @merwanroudane