I have a set of 7 assets, and I have run an ADF test on all possible pair-spreads to find possible pair strategies. I am creating the spreads using a rolling window in which I run linear regression to find the hedge ratio.
It seems that when the rolling window is large/long, few spreads are stationary. But as I decrease the size of the rolling window, more and more spreads becomes stationary. I feel like I'm somehow "cheating" or making a mistake, but I can't figure out what it is.
What is wrong about what I'm doing? Couldn't I take any pair of assets and make a "stationary" spread if I make the rolling window small enough?
EDIT: To be clear, the rolling window I'm referring to is the window of time in which I determine the hedge ratio.