The first attempt to obtain market directional information from non--stationary solution of the dynamic equation 1 "future price tend to the value maximizing the number of shares traded per unit time"  is presented. We demonstrate that price impact concept is poorly applicable to market dynamics and execution flow I=dV/dt operator with an "impact from the future" term , providing information about not yet executed tradesto be considered instead. 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)). The condition of "no information about the future" is found and directional predictions quality is discussed. This work make a substantial progress toward the solution of ultimate market dynamics problem: an evidence of existence (or a proof of non--existence) of an automated trading machine , consistently making positive P L trading on a free market as an autonomous agent , i.e. to decide whether market dynamics equation exist. Software with a reference implementation of the theory is provided.
A first attempt at obtaining market--directional information from a non--stationary solution of the dynamic equation "future price tends to the value that maximizes the number of shares traded per unit time" 1 is presented. We demonstrate that the concept of price impact is poorly applicable to market dynamics . Instead, we consider the execution flow I=dV/dt operator with the "impact from the future" term providing information about not--yet--executed trades. The " impact from the future " on I can be directly estimated from the already--executed trades, the directional information on price is then obtained from the experimentally observed fact that the I and p operators have the same eigenfunctions ( the exact result in the dynamic impact approximation p=p(I)). The condition for "no information about the future" is found and directional prediction quality is discussed. This work makes a substantial contribution toward solving the ultimate market dynamics problem: find evidence of existence (or proof of non--existence) of an automated trading machine which consistently makes positive P\&L on a free market as an autonomous agent (aka the existence of the market dynamics equation ). The software with a reference implementation of the theory is provided.
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