I have a question regarding the Pairs Trading strategy based on the Cointegration Approach. Most of the papers/literature I found on Pairs Trading using the Cointegration Approach are usually testing a given period for Cointegration (say 6 months) and then consider this pair for their trading strategy if the Cointegration Test suggests that the pair is cointegrated. In the papers they usually trade the next couple months (say 3 months) based on the assumption that the Cointegration from the 6 months testing period still holds.
Here is what I was wondering: (Assuming we use daily closing prices) instead of doing this test only once for the 6 months and then trading for the next 3 months, could we also check for Cointegration on a daily basis (rolling 6 months window) in the 3 months trading period? If so, why did none of the other papers do it in this way before?