fqardl 1.0.0

Initial CRAN Release (2026-02-25)

New Features

FQARDL (Fourier Quantile ARDL)

• fqardl() - Main function for Fourier Quantile ARDL estimation
• Automatic selection of optimal Fourier frequency (k*)
• Automatic lag selection using BIC, AIC, or HQ criteria
• Estimation across multiple quantiles (τ)
• Long-run and short-run multiplier computation
• PSS bounds test for cointegration
• Bootstrap cointegration testing
• Publication-ready plots

FNARDL (Fourier Nonlinear ARDL)

• fnardl() - Main function for asymmetric ARDL with Fourier terms
• Variable decomposition into positive/negative partial sums
• Wald tests for long-run and short-run asymmetry
• Dynamic multiplier computation (positive vs negative shocks)
• Cumulative multiplier visualization
• Asymmetry comparison plots

Helper Functions

• fourier_adf() - Fourier ADF unit root test
• generate_fourier_terms() - Generate Fourier trigonometric terms
• decompose_variables() - Decompose variables for NARDL
• perform_bounds_test() - PSS bounds testing
• bootstrap_bounds_test() - Bootstrap cointegration test

Visualization

• Coefficient plots across quantiles
• Dynamic multiplier plots
• Cumulative multiplier plots
• Persistence profile plots
• 3D coefficient surfaces
• Heatmaps
• Asymmetry comparison plots

References

• 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.

• Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In Festschrift in Honor of Peter Schmidt (pp. 281-314). Springer.

• Enders, W., & Lee, J. (2012). A unit root test using a Fourier series to approximate smooth breaks. Oxford Bulletin of Economics and Statistics, 74(4), 574-599.

• Cho, J. S., Kim, T., & Shin, Y. (2015). Quantile cointegration in the autoregressive distributed-lag modeling framework. Journal of Econometrics, 188(1), 281-300.

Acknowledgments

• Dr. Merwan Roudane for the original Stata implementation
• Rufyq Elngeh (رفيق النجاح) for supporting this development