I don't actually quite understand your question, but let me try here to explain the factor model.Multi-factor models like CAPM and Fama-French 3 are not just any general state-space/statistical factor model that you think about. By design and in the mind of Ross for APT, so-called Multi-factor models should be contemporaneous regression, using contemporaneous returns (or a realized value to exploit the correlation).You can try CAPM or FF3 using lagged return. R^2 is close to 0. It tells you the success of CAPM and FF3 is largely due to the contemporaneous corr in Unexpected Return. Do they help you predict into future? No, never. Even if CAPM holds, do you know what the market will be like tomorrow?If you want to predict return, this is the predictability literature. I think I just mentioned it in the forum. The best result is obtained by this guy,
http://faculty.chicagobooth.edu/bryan.k ... index.html, in Market Expectations in the Cross Section of Present Values. Predictability is about inferring EXPECTED return, not unexpected return, which accounts for the majority of realized return. Now you want to forecast volatility (this is also about expected volatility). It is known vol is persistent, so the forecasting variable could be past vol. Some people think skewness/kurtosis can also forecast vol. Results vary by paper. I am not aware of paper using fundamental to forecast vol. Note that fundamental variables are generally quarterly at most and subject to restatement. Quarterly reports are not audited, I think. Which vol do you want to forecast? Physical or RN? it is known that RN vol can forecast physical vol better than historical physical vol.