wavenardl

Wavelet-based Nonlinear Autoregressive Distributed Lag (W-NARDL) for Python

The first Python implementation of both standard NARDL and Wavelet-based NARDL models. This library provides a complete econometric toolkit for asymmetric cointegration analysis with wavelet denoising.

Features

Core Models

• NARDL — Nonlinear ARDL with short-run and long-run asymmetry (Shin et al., 2014)
• Wavelet NARDL — HTW wavelet-denoised NARDL (Jammazi et al., 2015)
• ARDL — Standard linear ARDL as a special case

Wavelet Methods

• Haar à Trous Wavelet (HTW) — Non-decimated transform from the paper
• PyWavelets Integration — SWT, DWT with any wavelet family
• Donoho Thresholding — Universal soft/hard threshold denoising

Statistical Tests

• PSS Bounds F-test — Pesaran, Shin & Smith (2001) with Cases I–V
• Narayan Test — Small-sample critical values (Narayan, 2005)
• Symmetry Tests — Wald tests for long-run and short-run asymmetry
• Diagnostics — Breusch-Godfrey, Breusch-Pagan, Jarque-Bera, RESET, CUSUM

Analysis Tools

• Dynamic Multipliers — Cumulative multiplier curves with bootstrap CI
• Long-run Coefficients — Delta method standard errors
• Error Correction Model — Two-step ECM estimation
• Automatic Lag Selection — Grid search, quick search (AIC/BIC/HQ)

Output & Visualization

• Publication Tables — LaTeX, HTML, and rich console output
• Wavelet Plots — Decomposition, scalogram heatmaps
• Multiplier Plots — Positive/negative effects with CI bands
• Diagnostic Plots — Residuals, Q-Q, ACF, CUSUM panels

Installation

pip install wavenardl

Or from source:

git clone https://github.com/mkeita/wavenardl.git
cd wavenardl
pip install -e .

Quick Start

Standard NARDL

from wavenardl import NARDL, pss_f_test, symmetry_test

import pandas as pd
data = pd.read_csv('my_data.csv')

# Estimate NARDL with asymmetric exchange rate effects
model = NARDL(
    data=data,
    formula="oil ~ exrate + cpi + Asymmetric(exrate) + deterministic(crisis)",
    maxlag=4,
    criterion='BIC'
)
results = model.fit(mode='grid')
results.summary()

# Cointegration test
pss = pss_f_test(results, case=3)
print(pss)

# Symmetry test
sym = symmetry_test(results)
print(sym)

Wavelet NARDL

from wavenardl import WaveletNARDL

# Fit W-NARDL with HTW denoising (as in the paper)
wmodel = WaveletNARDL(
    data=data,
    formula="oil ~ exrate + Asymmetric(exrate)",
    maxlag=4,
    wavelet_method='htw',  # Haar à Trous from the paper
    n_levels=4
)
results = wmodel.fit(fit_original=True)

# Compare original vs wavelet-denoised NARDL
results['comparison'].summary()

Dynamic Multipliers

from wavenardl import DynamicMultipliers, bootstrap_multipliers, plot_multipliers

# Compute multipliers
dm = DynamicMultipliers(results, horizon=40)
dm.summary()

# Bootstrap confidence intervals
mpsi = bootstrap_multipliers(results, horizon=40, replications=500, confidence_level=95)

# Plot
plot_multipliers(mpsi, variable='exrate', dep_var='oil')

Wavelet Visualization

from wavenardl import HaarATrousWavelet, plot_wavelet_decomposition, plot_scalogram

htw = HaarATrousWavelet(n_levels=6)
analysis = htw.full_analysis(data['oil'].values, name='Oil Price')

# Decomposition plot (paper Fig. 1 style)
plot_wavelet_decomposition(analysis)

# Scalogram heatmap
plot_scalogram(analysis, cmap='magma')

Publication Tables

from wavenardl import summary_table, comparison_table

# LaTeX table for journal submission
latex = summary_table(results, format='latex')
print(latex)

# HTML table for reports
html = summary_table(results, format='html')

Formula Syntax

The formula interface supports R-like specifications:

Dependencies

• NumPy, Pandas, SciPy, Statsmodels
• PyWavelets (pywt)
• Matplotlib
• Rich, Tabulate

References

• Jammazi, R., Lahiani, A., & Nguyen, D. K. (2015). A wavelet-based nonlinear ARDL model for assessing the exchange rate pass-through to crude oil prices. Journal of International Financial Markets, Institutions and Money, 34, 173-187.

• 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.

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

• Narayan, P. K. (2005). The saving and investment nexus for China. Applied Economics, 37(17), 1979-1990.

Author

Dr Merwan Roudane

License

MIT License