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Let's say you want to test the hypothesis that given a signal reaches some threshold, some asset will have some return over the next period.

Here we have two unknowns.

  • One, the value of your threshold - that triggers the trade
  • Two, the time period to measure your return after your signal occurs.

What approach do people usually take to solve the two unknowns? I've learned that data mining is bad (so I'm hesitant to test out random time periods and threshold values until I find a good combination), so what's a reasonable approach?

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This is a very tough problem and there are no definitive answers.

Of course you can try brute force, but you may very well overfit. One simple way to do this is to label each period in your time series with 1 if the return after X periods is above a desired threshold, 0 otherwise. Compute your strategy’s precision for a range of Xs. Then shift the labels by 1 (lag 1), do the same thing. Etc for many lags.

Or you can try to use more principled approaches, for instance methods that try to infer causality. This article is a good summary and has tons of interesting references.

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