Implementation of ARDL methods for cointegration analysis with
structural breaks and asymmetric effects. Includes: (1) Fourier Quantile
ARDL (FQARDL), quantile regression with Fourier approximation following
the quantile ARDL of Cho, Kim and Shin (2015)
Fourier ARDL methods for R: Fourier Quantile ARDL, Fourier Nonlinear ARDL, Multi-Threshold NARDL, and Fourier unit root tests.
CRAN: https://cran.r-project.org/package=fqardl
fqardl(bootstrap = TRUE) and fnardl(bootstrap = TRUE) are now recursive bootstraps (Bertelli, Vacca and Zoia 2022, or McNown, Sam and Goh 2018) with OLS conditional ECM statistics (Fov, t, Find), regressors and partial sums regenerated, Fourier terms held fixed, the Fourier frequency and lag orders re-selected in every replication, and the AND decision rule. The old scheme regressed a new Gaussian random walk on fixed regressors and declared cointegration when F or t rejected.mtnardl() is deprecated (removal in 2.0.0; use ardlverse::mtnardl()); its bounds F now uses only the lagged levels, thresholds other than 0 and cases other than 3 give an error.See NEWS.md for details and Monte Carlo evidence.
If you have produced results with fqardl 1.0.2 or earlier, please re-run them with 1.0.3 before relying on them.
Versions up to 1.0.2 estimated the wrong equation. fqardl, fnardl and mtnardl assembled a Pesaran, Shin and Smith conditional error-correction right-hand side but kept the dependent variable in levels rather than in first differences. The coefficient reported as the error-correction term was therefore 1 + rho instead of rho: positive and close to unity, with a large positive t ratio at every quantile.
| Quantity | Status in 1.0.2 |
|---|---|
| Error-correction term and its t ratio | Wrong sign; positive at every quantile |
| Long-run multipliers | Wrong sign and wrong magnitude in essentially every case |
| Bounds test F and t | Rejected the null almost unconditionally; the F was an average of squared marginal t ratios, not a Wald statistic |
| Verdict on cointegration | Binary; the inconclusive region was never reported |
| case = 1, 2, 4, 5 | Accepted but ignored; the design was always Case III |
| Lookups such as std_errors of y_lag1 | Returned NA silently |
Not affected: the Fourier frequency selection, the lag selection, and the partial-sum decomposition in fnardl and mtnardl.
On the package's own macro_data, the bounds statistic falls from F = 65.57, reported as "Evidence of cointegration", to F = 2.34, which is below the 5 percent lower bound of 3.79. In a simulation with a true long-run coefficient of +0.80, version 1.0.2 returned a median of -0.471 with the wrong sign in 100 percent of replications; 1.0.3 returns +0.791 with the correct sign in 100 percent of replications. On oil_gdp_data, fnardl previously reported an error-correction coefficient of +0.894 with t = +27.08; it now reports -0.106 with t = -3.21.
These now emit a warning at the point of use and are scheduled for 2.0.0. The bootstrap does not generate pseudo-samples under the null (corrected in 1.1.0). The cross-quantile Wald test assumes independence across quantiles and is therefore conservative. Quantile-specific bounds verdicts use critical values that Pesaran, Shin and Smith simulated for the conditional mean, so they should be read as descriptive.
Version 1.0.3 adds tests that assert the design's left-hand side equals Delta y, that the bounds F equals a hand-computed Wald statistic, that the estimator recovers a known long-run coefficient from simulated data, and that the shipped Case III critical values match Pesaran, Shin and Smith Tables CI(iii) and CII(iii) at 5 percent for every k from 1 to 10.
With thanks to Prof. Chi-Lu (Edward) Peng, National Kaohsiung University of Science and Technology, who reported the sign anomaly that led to this review.