Before revision:  An impact from the future  on I can be directly estimated from already executed trades, after that directional information on price can be obtained from experimentally observed fact that  I and p operators to have the same eigenfunctions (  exact result in  dynamic impact approximation p=p(I)).
After revision:  An impact from the future on I can be directly estimated from already executed trades, after that directional information on price can be obtained from experimentally observed fact that I and p operators to have the same eigenfunctions ( the exact result in dynamic impact approximation p=p(I)).