Version 1.0.1 — Now Available

Advanced Nonlinear ARDL
with Fourier & Bootstrap

A comprehensive Python library implementing NARDL, Fourier-NARDL, and Bootstrap Fourier-NARDL models for robust cointegration analysis and asymmetric effects estimation.

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Three Powerful Models

Choose the right model for your research needs, from standard NARDL to advanced bootstrap methods

📊

Standard NARDL

The foundational Nonlinear ARDL model based on Shin, Yu & Greenwood-Nimmo (2014). Decompose variables into positive and negative changes to capture asymmetric effects.

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🌊

Fourier NARDL

Extends NARDL with Fourier approximation for smooth structural breaks (Zaghdoudi et al., 2023). Capture gradual regime changes without specifying break dates.

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🔄

Bootstrap Fourier NARDL

Combines Fourier-NARDL with bootstrap cointegration tests (Bertelli et al., 2022). Eliminates the inconclusive zone problem of PSS bounds tests.

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Quick Start

Get up and running in minutes with our intuitive API


    

        
    

    Python


from nardl_fourier import NARDL, FourierNARDL, BootstrapNARDL

# Standard NARDL Model
model = NARDL(
    data=df,
    depvar='coal_consumption',
    exog_vars=['gdp', 'population'],
    decomp_vars=['oil_price'],
    maxlag=4,
    ic='AIC'
)

# View results
print(model.summary())

# Long-run multipliers
print(f"L⁺: {model.long_run['oil_price']['positive']['coefficient']:.4f}")
print(f"L⁻: {model.long_run['oil_price']['negative']['coefficient']:.4f}")

# Cointegration test
print(f"Bounds Test: {model.bounds_test['decision']['F_5%']}")

Key Features

Everything you need for professional econometric analysis

📈

Long-Run Multipliers

Compute and test asymmetric long-run effects with standard errors and confidence intervals using the delta method.

⚡

Dynamic Multipliers

Visualize the dynamic adjustment paths for positive and negative shocks with cumulative multiplier plots.

🧪

PSS Bounds Test

Test for cointegration with critical values for all cases and significance levels following Pesaran et al. (2001).

📋

Wald Asymmetry Tests

Formally test for short-run and long-run asymmetry with F-statistics and p-values.

📝

Publication-Ready Tables

Export results to LaTeX, HTML, or markdown formats ready for academic papers.

🔍

Comprehensive Diagnostics

Jarque-Bera, Breusch-Godfrey, Breusch-Pagan, CUSUM, and CUSUMSQ tests included.

Academic References

Built on rigorous econometric foundations

📚
Shin, Yu & Greenwood-Nimmo (2014)

"Modelling Asymmetric Cointegration and Dynamic Multipliers in a Nonlinear ARDL Framework"

📚
Zaghdoudi, Maktouf & Ochi (2023)

"Fourier Nonlinear ARDL Model for Smooth Structural Breaks"

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Bertelli, Vacca & Zoia (2022)

"Bootstrap cointegration tests in ARDL models" - Economic Modelling, 116, 105987