Looking at the sequence of negabinary representations, I could imagine (with the benefit of hindsight) that it wouldn't be too hard to guess the next numbers in the sequence. You'd just need to make a few observations: the rightmost digit always flips from 1 to 0. The second digit from the right reads one twice, then zero twice, etc. When you increase the length of the sequence, add two leading ones.

I'm not sure those would be enough, but just inspecting the digit-wise patterns would get you pretty far. Correctly interpreting the sequence is far harder!