R version 4.6.0 alpha (2026-04-03 r89785 ucrt) Copyright (C) 2026 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(testthat) > library(caustests) caustests 1.1.1 - Multiple Granger Causality Tests Type 'citation("caustests")' for citation information. > > test_check("caustests") ----------------------------------------------------------------- Panel Causality Test: PFTY H0: mvalue does NOT Granger-cause invest N = 5 panels, T = 20 periods, nboot = 99 ----------------------------------------------------------------- Fisher stat: 5.0086 df: 10 p-value: 0.8906 W-bar: 0.7563 Z-bar: -0.3853 p-value: 0.7000 Individual results: Panel Lag Freq Wald Boot p-val 1 1 1 2.5029 0.2929 2 1 1 0.0145 0.9697 3 1 1 0.1074 0.7980 4 1 1 1.1423 0.3838 5 1 1 0.0145 0.9394 ----------------------------------------------------------------- *** p<0.01, ** p<0.05, * p<0.10 ----------------------------------------------------------------- Panel Causality Test: PQC H0: mvalue does NOT Granger-cause invest N = 5 panels, T = 20 periods, nboot = 99 ----------------------------------------------------------------- Sup-Wald (mvalue => invest): 0.4392 Sup-Wald (invest => mvalue): 5.4955 Optimal lag: 1 Tau Wald(mvalue=>invest) p-val Wald(invest=>mvalue) p-val 0.25 0.4392 0.0100* 0.2188 0.0100* 0.75 0.0150 0.0100* 5.4955 0.0100* ----------------------------------------------------------------- *** p<0.01, ** p<0.05, * p<0.10 ----------------------------------------------------------------- Panel Cointegrating Polynomial Regression: Group-Mean FM-OLS (Wagner & Reichold 2023) Dep: invest | Poly: mvalue (degree 2) | N=5, T=20 ----------------------------------------------------------------- Variable Estimate Std. Err t-stat p-value ----------------------------------------------------------------- mvalue 0.7154 0.5885 1.2156 0.2241 mvalue^2 0.0017 0.0008 2.0782 0.0377** ----------------------------------------------------------------- Turning point x*: -214.1322 [95% CI: -736.5063, 308.2418] (U-shaped) Swamy S = 8.0000, df = 8, p = 0.4335 [Homogeneous] *** p<0.01, ** p<0.05, * p<0.10 ----------------------------------------------------------------- Panel Cointegrating Polynomial Regression: Group-Mean FM-OLS (Wagner & Reichold 2023) Dep: invest | Poly: mvalue (degree 2) | N=5, T=20 ----------------------------------------------------------------- Variable Estimate Std. Err t-stat p-value ----------------------------------------------------------------- mvalue 0.7154 0.5885 1.2156 0.2241 mvalue^2 0.0017 0.0008 2.0782 0.0377** ----------------------------------------------------------------- Turning point x*: -214.1322 [95% CI: -736.5063, 308.2418] (U-shaped) Swamy S = 8.0000, df = 8, p = 0.4335 [Homogeneous] *** p<0.01, ** p<0.05, * p<0.10 Individual FM-OLS Estimates (first 5 panels): Panel 1: 4.3875 -0.0009 Panel 2: -0.7292 0.0027 Panel 3: 1.7583 -0.0005 Panel 4: -1.1102 0.0044 Panel 5: -0.7292 0.0027 [ FAIL 0 | WARN 0 | SKIP 0 | PASS 48 ] > > proc.time() user system elapsed 1.35 0.18 1.53