The possibility of constructing universal nonlinear autoregressions

Autoregression models are widely used in economic practice both in modelling stochastic processes and in forecasting them. However, all these models generating nonlinear dependencies are essentially linear models. The accuracy of these models can be increased by giving them a nonlinear form. However, at present, there are no universal methods and techniques for forming such models, and the problem of constructing nonlinear autoregressions does not have a satisfactory solution. Researchers add non-linear components to autoregressions, most often using intuition. In our study, we examine the possibility of using the model of the elementary image of the Kolmogorov-Gabor polynomial as a formalized and universal tool for solving such problems. Several examples show that imparting nonlinearity to autoregression models can lead not only to an increase in the accuracy of approximation but also to an increase in the accuracy of short-term forecasting.