# Calibrating an Ornstein Uhlenbeck process on residuals of regression

I am trying a basic statistical arbitrage strategy as follows:

1. Perform PCA on a log return series of a basket of stocks
2. Regress returns against top principal components identified
3. Calculate the residuals of regression for each stock
4. Fit a OU process on the residuals

To fit an OU process, calculated the sum of residuals for each stock and regressed them on the lagged sum of residuals. However sometimes the intercept and slope are negative.

How do I calibrate this to an OU process when intercept or slope is negative?

• I don't know. Just slapping the $\Delta t$-factor onto the other factors doesn't seem to do the trick. Jan 6 '17 at 19:56