I am trying to use fundamental factors such as PE, BV, & CFO in a multivariate linear regression with the response variable being the rolling 1 month returns. But this approach seems flawed as the autocorrelation of the residuals is to high and the Durbin Watson test points also to such flaws. What is the best what to use long time horizon rolling returns in a linear regression?
Why not fit an ARMA model to the rolling returns first, and then model the residuals in your regression equation? That way you should be removing most of the effects of auto-correlation.
It simply points to the fact that your model as stands does not have much explanatory power of monthly returns. One reason could be of a observation period mismatch. I am not a fundamental type of guy, but I imagine that the monthly returns are measured over too short a period (1 month) while most fundamental factors are updated on a quarterly basis (sometimes semi-annually or annually depending on local market regulations). Thus, changes or absolute levels in cash flows on a quarterly basis may not be able to explain changes in monthly returns. Can you run the same model again but use quarterly returns (or match the periodicity of the independent variables periodicity) and report back?
Try fitting a model with ARMA errors?
However, if by "rolling returns" you imply a moving average of returns or some QoQ or YoY return series, which has much persistence, I am not so sure what the right way to proceed really is (with the exception that you can apply some corrections suggested in econometrics literature).