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Maybe there is a better choice, but here is what I think : take time series apply LOG function to each of them subtract MEAN or STDEV to standardize them (mean is less time consuming) Now you should have time series that are measured in the same units, thus, you can say for sure which one is higher and which is lower. The lower one you BUY, the higher - ...

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Yes, you're right. Choosing a fixed lookback period allows you to find more couple of candidates to implement a statistical arbitrages, but it is misleading, in the sense that, looking back, it leads you in finding the period in which a couple of assets are cointegrated and not a couple of assets are really cointegrated; So, what could be the solution to ...

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I think there is no quantitative method, but one can use some common sense based on how long one is willing to hold the position. For instance, if you don't want to hold a position in oil futures for more than a month, using a 10-year window is of no use even if the annual oil price is stationary. In practice, the trader probably tests a few windows whose ...

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