Testing Statistical Significance in Pairs Trading
Summary
The document asks how to test whether a pairs trading strategy has predictive power, and whether detrending methods used for other trading systems apply when the traded signal is already a linear combination of two price series. The answers outline two distinct questions: whether backtested returns exceed a chosen hurdle, and whether the candidate price series are cointegrated. They suggest standard return hypothesis tests for the former and Engle-Granger or Johansen procedures as starting points for the latter.
For strategy evaluation, the discussion recommends selecting pairs and tuning parameters on one period, then measuring performance on a later out-of-sample period. It illustrates rolling estimation and evaluation windows, followed by testing whether average pair performance differs from a benchmark such as zero. Bid-ask costs should be included. These are introductory suggestions rather than a complete testing protocol: the document does not specify test statistics, dependence adjustments, multiple-testing controls, or how to account for all forms of selection bias.
Key ideas
- Separate tests of strategy returns from tests of cointegration between asset prices.
- Use Engle-Granger or Johansen tests as initial tools for assessing cointegration.
- Select pairs and parameters using historical training data, then evaluate them out of sample.
- Test average pair performance against an explicit benchmark such as zero.
- Include bid-ask spreads when measuring strategy performance.
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Full text
# Statistical significance of a pair trading strategy # 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. ## Answer by Matt Wolf (score 4, accepted) https://quant.stackexchange.com/a/7129 - 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. ## Answer by Akavall (score 0) https://quant.stackexchange.com/a/7130 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.
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