GDP Dynamics as a Superposition of N. D. Kondratieff Technological Waves

A review of publications on the theory of long waves by Kondratieff–Schumpeter has shown that one of the imperfect elements of this theory in the case of modeling on their basis of GDP dynamics is the correlation of the dynamics of these waves with the dynamics of the observed values of GDP. The point is that the mathematical models currently used to describe periodic fluctuations in economic activity under this theory have a horizontal trend, and when moving to describe the growing (or declining) dynamics of GDP, it is necessary to include an exogenous trend that is not related to this theory in any way. This situation violates its integrity and often serves as one of the arguments against the adequacy of this theory to real economic processes. This article proposes a model of GDP dynamics based on the superposition of long Kondratieff waves and does not require the inclusion of exogenous trend. In this model, in addition to the generally accepted parameters of long waves, namely, the beginning and length of the wave period, two new parameters arise: the magnitude of its amplitude and the rate of change of this amplitude. These parameters allow you to configure the GDP model to describe the dynamics of the GDP of different countries, taking into account their real differences in the size of GDP. The problems of verification of the parameters of the proposed model arising in connection with the multi-extremality of the function describing this model are considered. Verification of the parameters of this model on specific data is carried out on the values of US GDP for the period from 1790 to 2018. The results of testing the model showed that the superposition of long Kondratieff–Schumpeter waves well describe the dynamics of US GDP over the entire period, and the model parameters are quite consistent with their generally recognized values.