For time series prediction I can rewrite the prediction problem in a standard Energy-minimization form. I used a Lyapunov based development of an energy function, with weights' change, therefore matrix derivation.
In order to achieve a more robust representation, I developed a new energy function by applying the standard quadratic penalties to the newly constructed restriction inequalities, and obtained:
with constants. Equation 2 states that the energy of the system depends only on the maximum error radius , as long as the restrictions are satisfied. If not, the terms , also contribute to the error function.
The basic idea of this approach is that not only controls all the other errors, but also ensures convergence by decreasing monotonously. If the maximum error(ME) radius decreases, so will all other errors contained in the error sphere. Which is more, the decreasing step is set by the decreasing step of the ME, that can be adjusted in order to assure convergence.