Breusch-Godfrey and Ljung-Box appear to be optimizations of Chi-Square. Recently I noticed a library in R that transforms a Chi-Square to a Phi Four Point Coefficient (
chisq_to_phi). Not being a full-blooded statistician this suggests a canonical rotation similar to transforming a t-test to a point-biserial correlation coefficient.
Could one transform either the Breusch-Godfrey or Ljung-Box test to a Phi Coefficient, given that they are related to Chi, using this function?
Could one square the resulting Phi Coefficient? Given that these tests estimate the likelihood that the remaining variability is different from white noise, would this further transformation (phi^2) index the variability remaining from a time series analysis in a meaningful manner?