Cointegration is a statistical property of certain types of data that indicates a strong relationship between them. When two variables are cointegrated, it means that they move together over time and tend to return to the same level after periods of divergence. This makes them ideal candidates for pairs trading, which is a popular strategy among hedge fund managers and other professional investors. Mathematically, the linear combination of two cointegrated time series is a stationary process, that is, a process with stable statistical properties.
Reference  discussed some issues regarding the use of cointegration in pairs trading,
An analysis of the possibilities of using cointegrated pairs for pair trading showed a number of problems that need to be solved for their successful use. The first problem associated with determining which period to take for analysis is more general than the problem of analyzing cointegrated pairs. This aspect is important for the analysis of any kind of time series. It seems promising to give more recent data more importance in the analysis, as, for example, is done with exponential smoothing.
Even if we assume that the cointegration ratio is stable, and we believe that it will not change in the future, then the question remains of determining the values of the entry and exit criteria for transactions and whether these criteria will change.
The next objective of the researchers should be to address the fact that the cointegration ratio or the presence of cointegration as a whole can alter (cointegration can “disappear”), and that this process must be anticipated (forecast). As a result, the trader must be given the conditions by which he can stop considering the pair to be cointegrated and stop using it for pair trading. If we assume that the cointegration ratio is constant and will not change in the future, the question of calculating the values of transaction entry and exit criteria as well as whether these criteria will change or remains.
We agree with the author and believe that the problems pertain not only to cointegration but any quantities that are calculated based on past price data.
Let us know what you think in the comments below.
 Rinat Faizullin, Problems of the use of cointegration pairs for pairs trading, http://bulletin.am/wp-content/uploads/2022/06/N2-2022-Bulletin-4.pdf
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