What exactly is group delay? I faintly remembered in college there was a class call Introduction To Group Theory which I didn't take for good reasons - too hard for me.I should have added that it is traditional moving averages used in the traditional way (ie crossovers) that don't work. Certainly, some of the newer low-lag MAs used in unconventional ways might work, but even then, it's a low probability proposition that they would. All of TA is a low probability proposition when price is very nearly a random walk.
Lag (or group delay) is what kills performance of MAs. Even a lag of half a sample period can really kill performance.