For a simple 2 variables (say X and Y) cointegration test, how does it affect our analysis, if we perform regression on X and Y with and without the intercept, and then test the spread for stationarity.
I am doing this analysis for stocks.
You're going to need an intercept, unless both your stocks start at 0! One stock will be a multiple of another, but then the first value in the history will always be a positive number.
Wait until you get into the time series component!
If X & Y are indeed co-integrated, then regressing X on Y will lead to spurious regression. So, I'm guessing your residuals will have a good amount of information which is not captured in the model.
But, I might have not understood some parts of your question well - When you say.. "how does it affect my analysis", it will help if you're a little more clearer about the specific problem because it seems as though you aren't doing time series analysis at all and are doing plain regression?
And, what do you mean by spread? Is it residual or something else?