I'm having some confusion doing Engle-Granger Cointegration test and then trade the ratio.
Methodology:
Run an OLS fit for A and B price time series without a constant. Therefore, $\hat{Y} = \gamma \cdot P_b + e$ where $\hat{Y}$ is the estimated stock A price and $P_b$ the price of stock B. The coefficient $\gamma$ would be the hedge ratio. Note that $e$ should have mean of 0 as white noise.
Get the residuals $S_t$ which is $Y - \hat{Y} = P_a - \gamma \cdot P_b = S_t $
Run ADF test over the $S_t$ series to determine if series are cointegrated.
If they are in fact cointegrated, how should the trades be made?
Compute the real ratio between the stock A and B prices $P_a/P_b$
Go long $1 \cdot A$ and short $\gamma \cdot B$? And viceversa if the signal is go short.
If I want to trade the spread, should I model the OLS as $ln(A) = -\gamma\cdot ln(B) + e $ ?
Thanks guys