Fourier Bootstrap ARDL Cointegration Test

Implements the Fourier Bootstrap Autoregressive Distributed Lag (FBARDL) bounds testing approach for cointegration analysis. Combines the Pesaran, Shin and Smith (2001) ARDL bounds testing framework with Fourier terms to capture smooth structural breaks, as in Yilanci, Bozoklu and Gorus (2020) , and recursive bootstrap critical values following McNown, Sam and Goh (2018) and Bertelli, Vacca and Zoia (2022) , with the Fourier frequency and the lags selected again in every bootstrap replication (a package choice); finite-sample bounds test critical values from Kripfganz and Schneider (2020) for models without Fourier terms. Features include lag selection via AIC/BIC, Fourier frequency selection by minimum SSR, long-run and short-run coefficient estimation and diagnostic tests.

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 and Smith (2001) ARDL bounds testing framework
• Fourier terms to capture smooth structural breaks (Yilanci et al., 2020)
• Recursive bootstrap critical values (McNown et al., 2018; Bertelli et al., 2022), with the Fourier frequency and the lags selected again in every replication (a package choice; or fixed by the user in advance)

The Kripfganz and Schneider (2020) bounds do not account for Fourier terms (in a Monte Carlo with independent random walks the 5% bounds decision rejected in 60.5% of samples), so with Fourier terms inference is by the bootstrap types and the bounds are used for decisions only in models without Fourier terms.

Installation

install.packages("fbardl")

# Development version
devtools::install_github("muhammedalkhalaf/fbardl")

Usage

library(fbardl)

# Load example data
data(fbardl_data)

# Fourier bootstrap ARDL (Bertelli, Vacca and Zoia scheme, the default);
# k* and the lags are selected again in each bootstrap replication
result <- fbardl(y ~ x1 + x2, data = fbardl_data, reps = 999, seed = 1)
summary(result)

# McNown, Sam and Goh scheme with k* and the lags fixed in advance
result_msg <- fbardl(y ~ x1 + x2, data = fbardl_data, type = "fbardl_mcnown",
                     kstar = 1, lags = list(p = 1, q = c(1, 1)), seed = 1)

# Bounds test (valid without Fourier terms only)
result_bounds <- fbardl(y ~ x1 + x2, data = fbardl_data, type = "fardl",
                        fourier = FALSE)

Test Types

Features

• Automatic lag selection via AIC or BIC
• Fourier frequency selection by minimum SSR over integer frequencies (default) or a fractional grid
• Three cointegration tests: F-overall, t-dependent, F-independent
• Degenerate case detection (McNown et al., 2018; cases numbered as in Bertelli et al., 2022)
• 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 (R-squared, AIC, BIC)

References

• Bertelli, S., Vacca, G. and Zoia, M. (2022). Bootstrap cointegration tests in ARDL models. Economic Modelling, 116, 105987. https://doi.org/10.1016/j.econmod.2022.105987

• Enders, W. and 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. https://doi.org/10.1111/j.1468-0084.2011.00662.x

• Pesaran, M. H., Shin, Y. and 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. and 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. and 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. and 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