  In this paper we consider high dimension models based on dependent
observations defined through autoregressive processes. For such models we
develop an adaptive efficient estimation method via the robust sequential model
selection procedures. To this end, firstly, using the Van Trees inequality, we
obtain a sharp lower bound for robust risks in an explicit form given by the
famous Pinsker constant. It should be noted, that for such models this constant
is calculated for the first time. Then, using the weighted least square method
and sharp non asymptotic oracle inequalities we provide the efficiency property
in the minimax sense for the proposed estimation procedure, i.e. we establish,
that the upper bound for its risk coincides with the obtained lower bound. It
should be emphasized that this property is obtained without using sparse
conditions and in the adaptive setting when the parameter dimension and model
regularity are unknown.
