The rate of world GDP is changing periodically. A discrete dynamic model (DDM) describes this process. The model is based on the assumption that the global economy has certain “inertia”. This allows us to describe the rate of change of global GDP in the subsequent year as a function of its change in the preceding year. This function can be approximated by using a finite number of terms of its Taylor series. A methodologically more rigorous approach is proposed for approximating the rate of world GDP change on non-overlapping time intervals. Radii of convergence were determined for approximating polynomials for these time ranges. Studies have shown the dependence of the shape of the radius of convergence from the nature of the convergence. DDM has a practical significance because it allows identifying the change in a character of economic dynamics without prior assumptions about the factors driving this trend.