Obviously, well written HFTs avoid this by introducing some hysteresis to the signal. i.e. Insert an order when the signal crosses 0.5, but then only delete it if the signal falls below 0.4.

Chris: You've also missed the most common cause of these issues in my experience - feedback from identifying your own orders in the public stream. HFTs need to filter their own orders out of the orderbook they are trading on, or a feedback loop can begin. This can be difficult, since some exchanges don't provide a clear way to identify your own order, or it may be the case that you receive the public UDP packet before the private TCP packet that contains the ID required to match the two.

For example (a basic one), say I have an algo that calculates the midpoint based on the best bid and ask volumes. And can only insert within x distance of the midpoint. I add a bid to the top of the book for a 1 lot, get the UDP public depth update, don't know whether this is my order or someone elses. So I re-calculate the midpoint, which pushes the midpoint upwards (greater bid volume), which means I then pull my bid, which means I recalculate the mid again, then re-insert, etc. etc....