To limit false positives, we've found that it is key to apply accurate statistical models to these data. In particular, modelling the tails of probability distributions accurately is key to reducing false positives. In addition, automatically modelling the periodic and seasonal components means that you can model the residuals, which again improves accuracy.
Finally, we've found that normalising the results allows the signal to noise ratio to be controlled, providing an accurate ranking of results in highly anomalous environments.
Happy to provide more customer examples as required.