We have constructed a return factor for a Fama-French-Carhart type factor model which adds a "BMG" factor for climate risk exposure (see open-climate-investing)
This BMG factor is orthogonalized based on regression of returns of 2 ETF's against interest rate variables. Periodically the regression coefficients should be updated, but how should we do it so that it's not "jerky"--ie, a sudden change in the factor series when we decide to update the variables every year?
One idea is to run the regression for the previous 60 months of returns every month, and then set use the rolling average of the last 6 or 12 month regressions, so that we smooth out the change in the orthogonalization.
Does this sound reasonable? Have you seen other ways to do this?