My question is dealing with the proportionality between Dividend Index Futures prices and Index prices. Indeed, we in the past we used to do a simple regression between these variables and use the same $\beta$ factor for future forecasts.
But, we observe that in Bull market, the dividends tends to cap, and thus the usage of the previous $\beta$ will lead to misforecasting and mishedge. While during Bear market the $\beta$ increases.
I would like to know if you have already seen in the literature something like this, and how would you deal with this to provide better estimations or regression between the two previous variables (or their returns)!