# Statistical significance of a pair trading strategy

How can I test the significance of a pair trading strategy, i.e. that the H0 is "The strategy has no predicting power".

I was considering to use the technique in Evidence Based Technical Analysis that test the strategy against a benchmark built by detrending the price series, but I think that this doesn't work in the pair trading strategy because the linear combination of the two price series is already detrended.

• if you just want to test for significance of the generation of returns exceeding a hurdle rate then you can just setup a standard hypothesis test where you test whether your returns you generate from back tests exceeds a certain return.

• if you are more interested in testing for co-integration then you should consider the Johansen and/or Engle-Granger tests for starters.

• Thanks Freddy. How can I set that hurdle rate, can it just be 0? Commented Jan 28, 2013 at 15:10
• @VictorP, entirely depends on what you try to test for. For example, lets say you generate gross returns ex. execution related expenses. Then as hurdle rate you may want to set a rate that at the very least overcomes your trading related cost. Or you may want to set a rate that exceeds a certain required return set forth by a benchmark rate. The choice is entirely yours. Commented Jan 28, 2013 at 15:14

Do you have a specific strategy in mind? If so can use past data to identify the pairs you want to trade, and parameters (e.g. how big should the spread be before you buy/short) using your strategy, then use this results on the out of sample period. For example:

You have 1000 daily observations. You use 0 to 250 to select pairs and parameters, than you use test how they perform in period 250 to 500. Then you use 250 to 500 to select pairs and parameters and test them in 500 to 750 and so on...

You can see how well your strategy performed by recording performance of every pair and testing that the mean of those performances is different from 0 (if you want to test against 0). Make sure that you are taking bid-ask spread into account.

• Thanks Akavall. My problem in this approach is that the out-of-sample is only one of many possible outcomes, and that is not enough to deny the null hypothesis. Commented Jan 28, 2013 at 20:22
• @VictorP, why is it only one outcome? Even if you only have two periods, you can record profit from each pair, so if your strategy selected 50 pairs to trade, you will have profits from each pair, that is you would have to test if the mean of 50 observations is different from zero. Commented Jan 29, 2013 at 2:17