Fourier Bootstrap ARDL Cointegration Test

Implements the Fourier Bootstrap Autoregressive Distributed Lag (FBARDL) bounds testing approach for cointegration analysis. Combines the Pesaran, Shin & Smith (2001) ARDL bounds testing framework with Fourier terms to capture structural breaks following Yilanci, Bozoklu & Gorus (2020) , and bootstrap critical values based on McNown, Sam & Goh (2018) and Bertelli, Vacca & Zoia (2022) , with finite-sample bounds test critical values from Kripfganz and Schneider (2020) . Features include automatic lag selection via AIC/BIC, optimal Fourier frequency selection by minimum SSR, long-run and short-run coefficient estimation, diagnostic tests, and dynamic multiplier analysis.

fbardl: Fourier Bootstrap ARDL Cointegration Test

R implementation of the Fourier Bootstrap ARDL (FBARDL) bounds testing approach for cointegration analysis.

Overview

The fbardl package combines:

• Pesaran, Shin & Smith (2001) ARDL bounds testing framework
• Fourier terms to capture smooth structural breaks (Yilanci et al., 2020)
• Bootstrap critical values for robust inference (McNown et al., 2018; Bertelli et al., 2020)

Installation

# Install from source
install.packages("fbardl_1.0.0.tar.gz", repos = NULL, type = "source")

# Or using devtools
devtools::install_github("muhammedalkhalaf/fbardl")

Usage

library(fbardl)

# Load example data
data(fbardl_data)

# Basic Fourier ARDL test
result <- fbardl(y ~ x1 + x2, data = fbardl_data, type = "fardl")
summary(result)

# Bootstrap ARDL (McNown approach)
result_boot <- fbardl(y ~ x1 + x2, data = fbardl_data,
                      type = "fbardl_mcnown", reps = 999)
summary(result_boot)

# Without Fourier terms
result_nofourier <- fbardl(y ~ x1 + x2, data = fbardl_data, fourier = FALSE)

Test Types

Features

• Automatic lag selection via AIC or BIC
• Fourier frequency selection by minimum SSR
• Three cointegration tests: F-overall, t-dependent, F-independent
• Degenerate case detection (McNown et al., 2018)
• Long-run coefficient estimation via delta method
• Diagnostic tests: Jarque-Bera, Breusch-Godfrey, Breusch-Pagan, ARCH

Output

The function returns an object of class "fbardl" containing:

• Model coefficients and standard errors
• Long-run and short-run coefficient estimates
• Cointegration test statistics and p-values
• Diagnostic test results
• Model fit statistics (R², AIC, BIC)

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. https://doi.org/10.1002/jae.616

• McNown, R., Sam, C. Y., & Goh, S. K. (2018). Bootstrapping the autoregressive distributed lag test for cointegration. Applied Economics, 50(13), 1509-1521. https://doi.org/10.1080/00036846.2017.1366643

• Yilanci, V., Bozoklu, S., & Gorus, M. S. (2020). Are BRICS countries pollution havens? Evidence from a bootstrap ARDL bounds testing approach with a Fourier function. Sustainable Cities and Society, 55, 102035. https://doi.org/10.1016/j.scs.2020.102035

• Kripfganz, S., & Schneider, D. C. (2020). Response surface regressions for critical value bounds and approximate p-values in equilibrium correction models. Oxford Bulletin of Economics and Statistics, 82(6), 1456-1481. https://doi.org/10.1111/obes.12377

Author

Muhammad Alkhalaf ([email protected])

License

GPL-3