A Gabor--Epps uncertainty principle for traders

Abstract

We propose a Gabor--Epps uncertainty principle for practical trading. The key idea is that high-frequency correlation is not observed in clock time alone, but is resolved through market activity, order-flow overlap, and finite coupling response. This suggests six simple rules of thumb that may be useful to traders and trading programs operating at market-making frequencies, particularly those crossing books and markets below the average human response time. Throughout, the observation window is clock-dependent: in calendar time it is a physical interval, in trade time it is a trade-count interval, and in volume time it is a volume bucket. In summary: at event scales, the more precisely one localises market activity in time, the less well one can resolve stable cross-asset dependence. The more one resolves dependence, the more one has coarse-grained away the event-time structure that generated it. This can generate substantial clock risk.