# How to measure clustering in time duration?

I wish to measure clustering in the duration between stock trading. For example, a trade occurs at 1:59:19 and the next trade follows at 1:59:23 - the inter-trade duration is 4 seconds. I have roughly 50,000 trades per day for a particular stock. I was told that I can square the inter-trade duration in order to capture clustering in trades. Is this correct? What if I have a lot of trades that occur at the same time? Hence, inter-trade duration is 0 seconds. Can this have an impact on my clustering measure?

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It's straightforward to compute, so obviously, you can do it.

But I don't know a reason why you should take the squared delays. Is $s^2$ a sensible score here? To me this sounds like a heuristic.

Define "correct". I don't see any notion of correctness involved here. It may work for some, it may not work for others. It may be sensible for some use case, or it might not. This is more of a personal preference than a mathematical truth.

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