fqardl 1.0.5

fqardl 1.0.4

An adversarial audit of 1.0.3 was run before submitting it to CRAN: fifty-three checks that try to break the release rather than confirm it, including an external oracle that rebuilds the model from scratch with quantreg, a falsification test that re-introduces the old defect and requires the old symptom to return, an empirical size study under a no-cointegration null, and a sweep of thirty-six combinations of k, p and q. Two findings came out of it, one of them in my own repair.

Corrected

The 1 and 10 percent critical values in 1.0.3 had no traceable provenance

Version 1.0.3 shipped a Case III table with 1, 5 and 10 percent points and stated in a comment that the 1 and 10 percent columns were “inherited from 1.0.2”. The audit checked that claim and it was false: those entries match neither 1.0.2 nor anything I can tie to Pesaran, Shin and Smith. Only the 5 percent column was ever verified.

Shipping plausible-looking numbers of unknown origin is exactly the fault this whole line of releases exists to correct, so the 1 and 10 percent F bounds are now returned as NA, as the 1 and 10 percent t bounds already were. The decision rule uses the 5 percent level only, and get_pss_critical_values() now returns a verified flag saying which entries are backed by the source. A test asserts it.

For the record: 1.0.2’s own Case III table was wrong for every k >= 2

The audit compared the shipped table against 1.0.2’s. They agree at k = 1 and diverge everywhere else, and for k > 6 version 1.0.2 returned a single default row for every k:

k 1.0.2, 5 percent Table CI(iii), 5 percent
1 4.94 / 5.73 4.94 / 5.73
2 3.55 / 4.38 3.79 / 4.85
3 3.10 / 3.99 3.23 / 4.35
5 2.69 / 3.61 2.62 / 3.79
7 to 10 2.48 / 3.34 for all 2.32/3.50 down to 2.06/3.24

At k = 2, version 1.0.2 compared against an I(1) bound of 4.38 where the paper gives 4.85. That made rejection easier for a second reason entirely independent of the levels-versus-differences defect, and it was not mentioned in the 1.0.3 notes because it had not yet been found. The 1.0.3 release notes also quoted 4.38 as though it were correct; that wording is corrected above.

Verification

Fifty-three adversarial checks pass and none fails. The ones worth naming:

The audit script ships as ADVERSARIAL.R so that anyone can re-run it.

A note on what remains unverified

Being explicit, because the point of this release is that unverified numbers do not ship silently: the 5 percent column of Tables CI(iii) and CII(iii) is checked against the source for every k from 1 to 10. Nothing else in the critical-value tables is. Cases I, II, IV and V are not available. The bootstrap null and the cross-quantile covariance remain as described under 1.0.3.

fqardl 1.0.3

This is a correctness release. Results change. Anyone who has run version 1.0.2 should re-run their analysis before relying on it.

The defects below came to light after a question from Prof. Chi-Lu (Edward) Peng, National Kaohsiung University of Science and Technology, who noticed that the bounds-test t statistic was positive at every quantile when it should be negative. Our thanks to him for reporting it.

Corrected

The estimated equation had an error-correction right-hand side and a levels left-hand side

build_ardl_design(), estimate_nardl() and estimate_mtnardl() assembled a Pesaran, Shin and Smith conditional error-correction design on the right-hand side, containing the lagged levels y_{t-1} and x_{t-1} together with the differences Delta y_{t-j} and Delta x_{t-j}, while setting the left-hand side to y_t in levels rather than Delta y_t. The equation actually estimated was therefore the conditional levels ARDL.

Hence the coefficient reported as the error-correction term was phi = 1 + rho rather than rho. Since rho lies in (-1, 0) under cointegration, the reported coefficient was positive and close to unity, with a large positive t ratio at every quantile.

The defect propagated:

The “F statistic” was not a Wald statistic

perform_bounds_test(), perform_nardl_bounds_test() and perform_mtnardl_bounds() computed mean(t^2) over the terms matching _lag1$, that is, the arithmetic mean of the squared marginal t ratios. That ignores the covariances among the level coefficients, has no distribution theory, and was being compared against tables that Pesaran, Shin and Smith simulated for a genuine Wald statistic.

All three now compute the Wald form of PSS equation (21), W = (Rb)' (R V R')^{-1} (Rb), with F = W / (k+1) for Case III.

The inconclusive region was not reported

The bounds procedure has three outcomes, not two. When the statistic falls between the I(0) and I(1) bounds, inference is inconclusive without knowing the cointegration rank of the regressors. Version 1.0.2 collapsed this into a binary verdict. All bounds routines now return a three-way decision.

The bounds test is now computed at every quantile

perform_bounds_test() located tau = 0.5, computed one statistic there, and reported it as though it were general. It now returns a per-quantile table in $summary, with the median quantile promoted to the top level so that code written against the 1.0.2 return shape keeps working.

case was accepted and never used

fqardl() validated case and then ignored it: the design matrix was always Case III (unrestricted intercept, no trend) while the critical values were switched. Cases 4 and 5 therefore compared a Case III model against Case IV and Case V tables, and case = 3 and case = 5 returned identical coefficients. Any case other than 3 now raises an error. Correct case handling changes the regressors, not the table, and is scheduled for 2.0.0.

Standard errors were unnamed, so lookups returned NA silently

In estimate_qardl() the coefficient vector was renamed to the design column names while the standard-error and t-statistic vectors were not. Any lookup such as std_errors["y_lag1"] returned NA without warning. All three vectors are now named consistently.

Critical-value table

The Case III tables are stated explicitly and checked by a test. The 5 percent column of Tables CI(iii) and CII(iii) has been verified against the published table for every k from 1 to 10. The 1 and 10 percent columns of CI(iii) are inherited from earlier versions and have not been independently verified; the 1 and 10 percent I(1) bounds of CII(iii) are returned as NA rather than guessed. Only the 5 percent level is used in the decision rule.

Smaller fixes

Known limitations, documented rather than silently shipped

Each of these now raises a warning at the point of use. All are scheduled for 2.0.0.

  1. bootstrap_bounds_test() does not generate pseudo-samples under the null. The McNown, Sam and Goh (2018) procedure requires each of the three statistics to have its own restricted residuals, and requires the level series to be built by accumulation, y*_t = y*_{t-1} + Delta y*_t. Neither is done. The p-values are indicative only.
  2. quantile_wald_test() assumes independence across quantiles. Quantile-regression estimates from the same sample have covariance proportional to min(tau_i, tau_j) - tau_i tau_j, which is strictly positive, so the correct denominator is smaller than the one used. The test is conservative and under-rejects constancy. Fixing it requires the joint cross-quantile covariance, which this release does not compute.
  3. Quantile-specific bounds verdicts have no distribution theory. The PSS critical values were simulated for the conditional mean. Treat the per-quantile table as descriptive.
  4. Deterministic cases I, II, IV and V are not available.

Verification

This release ships verify_fqardl_103.R, sixteen checks, all passing, including:

fqardl 1.0.0

Initial CRAN Release (2026-02-25)

New Features

FQARDL (Fourier Quantile ARDL)

FNARDL (Fourier Nonlinear ARDL)

Helper Functions

Visualization

References

Acknowledgments