ardlverse

• mtnardl(auto_select = TRUE, n_thresholds = 1) always returned 0 because the internal call failed silently; it now returns the threshold that minimises the AIC over 0 and the deciles of the changes.
• mtnardl(): asymmetry_tests[[v]] gains an element joint (Wald test of equal level coefficients across all regimes, chi-squared with R - 1 degrees of freedom) and every test a field df.
• boot_ardl(), aardl() and mtnardl() used all.vars() on the formula, which silently turned log(y) ~ log(x) into y ~ x; transformed terms and interactions now give an informative error. Missing values give an error instead of being dropped (dropping rows closed gaps in the series).
• boot_ardl(), aardl() and mtnardl() called set.seed() on the session's generator; the seed is now used locally and the caller's random number state is restored.

New features

• New exported function fbnardl(): Fourier (bootstrap) nonlinear ARDL with positive and negative partial sums, selection of the Fourier frequency (integer frequencies chosen by minimum SSR as in Enders and Lee (2012, Oxford Bulletin of Economics and Statistics) by default, or a fractional grid) and of the lags by AIC or BIC on a common sample, Kripfganz and Schneider (2020) bounds without Fourier terms, recursive bootstrap with the frequency and lags selected again on every bootstrap sample (package choice; BVZ step 5(c) re-estimates the unrestricted model but does not discuss re-selection; or fixed with kstar and lags), delta-method long-run coefficients and symmetry test, a short-run symmetry test on the sum over lags, cumulative dynamic multipliers by full recursion with parametric bands, and diagnostics. With bootstrap = "bvz" the default x model is the marginal model of BVZ eqs. 19-20 (xdgp = "vecm"); xdgp = "rw" regresses the differences on the intercept, Fourier terms and exog only (a package choice). bootstrap = "mcnown" uses the Fov null for all statistics applied to the conditional ECM (package choice). The R code is a port written for this package, following the Stata module fbnardl; it corrects the long-run Wald gradient (13.36 instead of 631.90 in the reference example), the fixed-design bootstrap, the hard-coded asymptotic case III bounds, the use of bounds with Fourier terms, the lag selection on different samples, the multipliers without lagged short-run terms (0.928 instead of 0.986 at horizon 1 in the reference example), and the storage of failed replications as 0 found in the stand-alone version 1.0.2. Rejection rates with the frequency and lags selected again in each bootstrap sample (package choice; BVZ step 5(c) re-estimates the unrestricted model but does not discuss re-selection): 7.0% (1.8%) (Fov), 11.5% (2.3%) (t), 11.5% (2.3%) (Find), 3.5% (1.3%) for a "cointegration" decision (stand-alone 1.0.2: 98.5% (0.9%), 99.0% (0.7%), 67.5% (3.3%)).
• mtnardl(): long-run coefficients with delta-method standard errors computed with the full covariance matrix (long_run_table), delta-method differences of the long-run coefficients between regimes (lr_differences), the Find statistic, decompose (a subset of regressors to decompose; the others enter linearly) and threshold_type = "quantile" (thresholds given as probabilities and converted to quantiles of the changes of each variable), which give a migration path from fqardl::mtnardl().
• New internal file R/ardl_boot_engine.R (engine version 1.1.0): the recursive bootstrap engine shared by all bootstrap tests, with a reproduction check (the recursion with the original residuals reproduces the data), a design check (the bootstrap model equals the estimated model), failed replications stored as NA with a warning and counts, order-statistic critical values and the combined decision. With a random block of initial values the partial sums continue the data's levels in the block, so the generating model is the estimated restricted model. The x equation has p lags of the differences when the y equation has p lagged differences of y (BVZ eq. 19). The argument j0 = 1 gives the unconditional y equation of MSG eq. 12 (no contemporaneous differences). Recentring once (MSG eq. 13) subtracts the residual mean: eq. 13 divides the sum of the residuals by n - q - 1, the number of residuals of their ARDL(1,1) model, and applies no rescaling factor.

Other changes

• DESCRIPTION: "bootstrap-based bounds testing per Pesaran, Shin and Smith (2001)" replaced by a description of the bounds test with Kripfganz and Schneider (2020) critical values and recursive bootstrap critical values (Bertelli, Vacca and Zoia, 2022; McNown, Sam and Goh, 2018).
• boot_ardl() documentation: it no longer claims to follow McNown, Sam and Goh (2018) for a scheme that differed from it, documents that F_overall equals F_stat, and documents the decision rule. aardl() documentation no longer attributes its bootstrap to McNown, Sam and Goh (2018) and Sam, McNown and Goh (2019).
• The start-up message showed version 1.0.0; it now shows the installed version.
• Examples run with small numbers of bootstrap replications.
• Tests: statistics against independent lm()/anova() computations, bootstrap draws against an independent recursion (BVZ with partial sums and a random block; MSG joint null), and size Monte Carlo tests (skipped on CRAN) for boot_ardl(), aardl(), mtnardl() and fbnardl().

Pending verification

The following papers were not available for this release; the choices below are documented as package choices:

• Pal and Mitra (2016) and Shin, Yu and Greenwood-Nimmo (2014): k in the bounds of mtnardl(), regime formation, multiplier definition and sign convention for negative partial sums, the short-run symmetry test on the sum over lags in fbnardl().
• Yilanci, Bozoklu and Gorus (2020) and Omay (2015): the fractional frequency grid of fbnardl() and its validity; the default is the integer grid.
• Sam, McNown and Goh (2019): bootstrap details of the augmented ARDL test in aardl().