On functional definition of time-series models

We present a discussion on a class of econometric models for time series given implicitly as a solution of a system of functional equations. Particularly, processes AR, ARMA, ARCH, GARCH are models of such a structure. These nonlinear time series models are treated from several points of view. Task of existence of a solution, possibility of numerical simulations and description of solutions are considered and partially solved in the article.