Nonlinear vector autoregressions in short-term metal price forecasting

 In order to make an effective economic decision, it is necessary to have an idea of the possible future state of the decision-making object and its environment, which is obtained by means of forecasting. The more accurately forecasts are performed, the less uncertainty in the decision-making situation, and the more effective the decisions made. Therefore, improving the accuracy of economic forecasting is an important scientific task. One of the new directions in economic forecasting is forecasting with the help of vector autoregression models. But the practical application of these models is difficult, because with increasing dimensionality of the autoregression vector the number of model coefficients grows nonlinearly and there are serious computational difficulties in the construction of such models. We propose to use complex-valued vector autoregressions, which are simpler than vector autoregressions of real variables, because they contain half the number of coefficients, the values of which should be estimated by statistical methods. Using the example of the market of world prices for non-ferrous metals, we have formed an eight-dimensional vector of prices for non-ferrous metals, precious and non-precious. Two linear vector autoregressions of real and complex variables, as well as two nonlinear models of vector autoregressions of real and complex variables were constructed on the basis of statistical data of this vector. It is shown that the nonlinear complex-valued vector autoregression is the best model of these four models both from the positions of Bayesian information criterion and from the position of accuracy of short-term economic forecasting, which was verified using the latest statistics. It is recommended to use nonlinear complex-valued autoregressions for short-term economic forecasting of prices. The possibility of using complex-valued vector autoregressions in short-term forecasting of other economic indicators should be clarified through additional research using the methodology outlined in the article. Proving the effectiveness of using complex-valued vector autoregressions in short-term economic forecasting is the basis for further construction of complex-valued vector autoregression models of dimensions greater than 10, which is extremely difficult or impossible for vector autoregressions of real variables.