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 (muhammedalkhalaf@gmail.com)

License

GPL-3