caustests 1.1.4

• xtpcmg(): the one-sided long-run covariance used in the fully modified bias correction was transposed (it estimated the sum of E(u_t v_{t+j}) instead of E(v_t u_{t+j})), and the quadratic spectral and Daniell kernels did not use the one-sided weights of the authors’ code; group-mean and pooled FM-OLS estimates were therefore biased. The long-run covariance now follows the authors’ lr_varmod.m.
• xtpcmg(), pooled model: the covariance matrix is now the asymptotic covariance of de Jong and Wagner (2022) for one-way and two-way effects (as in the authors’ PanelEKC code), with a heteroskedasticity-robust sandwich for the controls; the previous version used sigma^2 (X’X)^-1 from the FM residuals, and a unit matrix when X’X was singular.
• xtpcmg(), cross-section robust covariance (corr_rob = TRUE): uses the conditional long-run covariance between units instead of the covariance of u alone.
• All xtpcmg() estimates and standard errors now reproduce the Stata module xtpcmg 1.0.2; tests added.

caustests 1.1.3

• Bug fix: in the Toda-Yamamoto type tests (1, 3, 5, 6 and 7) the lag order was selected on the VAR augmented with the extra dmax lags, so the selected p was that of the augmented model. The lag order p is now selected on the VAR in levels with p lags, and the test VAR then has p + dmax lags, as in Toda and Yamamoto (1995).
• Bug fix: the Fourier terms were evaluated on a time index that restarted at 1 after the lags were dropped, so sin(2 pi k t / T) was shifted and scaled by the effective sample size. They now use the time index t = 1, …, T of the full sample, in the selection step as in the test regression.
• With these changes the Wald statistics, lags and frequencies of tests 1 to 5 agree with the Stata command caustests (SSC) on the same data (for example 9.326 for test 1 and 21.944 for test 2).

caustests 1.1.2

• Corrected the DOI of Wang and Nguyen (2022) to 10.1080/1331677X.2021.1948436.
• Removed a DOI attached to de Jong and Wagner (2022) that could not be verified in CrossRef; the citation text is unchanged.
• No changes to code.

caustests 1.0.0

Initial CRAN Release

• Implemented 7 Granger causality tests:
  • Test 1: Toda-Yamamoto (1995)
  • Test 2: Single Fourier Granger (Enders & Jones, 2016)
  • Test 3: Single Fourier Toda-Yamamoto (Nazlioglu et al., 2016)
  • Test 4: Cumulative Fourier Granger (Enders & Jones, 2019)
  • Test 5: Cumulative Fourier Toda-Yamamoto (Nazlioglu et al., 2019)
  • Test 6: Quantile Toda-Yamamoto (Cai et al., 2023)
  • Test 7: Bootstrap Fourier Granger Causality in Quantiles (Cheng et al., 2021)
• Features:
  • Automatic lag order selection via AIC or BIC
  • Optimal Fourier frequency selection
  • Bootstrap inference for robust p-values
  • Support for multivariate systems (all pairwise directions)
  • Quantile causality testing across distribution
• S3 methods: print(), summary(), plot()
• Example dataset: caustests_data

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