Checking for model consistency in optimal fingerprinting: a comment

Abstract Allen and Tett (1999, herein AT99) introduced a Generalized Least Squares (GLS) regression methodology for decomposing patterns of climate change attribution purposes proposed the “Residual Consistency Test” (RCT) to check GLS specification. Their has been widely used highly influential ever since, in part because subsequent authors have relied upon their claim that model satisfies conditions Gauss-Markov (GM) Theorem, thereby yielding unbiased efficient estimators. But AT99 stated GM Theorem incorrectly, omitting critical condition altogether, method cannot satisfy conditions, variance estimator is inconsistent by construction. Additionally, they did not formally state null hypothesis RCT nor identify which it tests, prove its distribution values, rendering uninformative as specification test. The continuing influence two decades later means these issues should be corrected. I 6 needing shown valid.