Is it possible to estimate the optimal look back period for OLS from which we test if residuals are stationary? Almost all papers that I read use random look back periods of 100 days, 252 days, 500 days etc.
I think this procedure introduces data snooping bias.
The only "quantitative" method that I've found so far is calculation half-life of mean reversion and using it as a look back period.
Can somebody suggest a methodology or a procedure to select the optimal length of a look back period which can be used to test if a pair of stocks is co-integrated?
Any help will be appreciated.