Method for Constructing Vector Autoregressions of Any Complexity

Vector autoregressions are one of the rapidly developing areas of many areas of modern science. They are actively used in modeling and forecasting various economic processes, most often in modeling the stock market and retail prices. Their most important advantage is the ability to consider the simultaneous influence of modeled indicators not only from their past values, but also from the past values of other indicators interrelated with them. The main problem why vector autoregressions are not actively used in practice (as they deserve) is the “curse of dimensionality†, which consists in a quadratic increase in the number of model coefficients depending on the increase in the dimension of the modeled vector. This circumstance leads to the fact that researchers in various fields of modern science are forced to limit the dimension of the vector, including only the most important ones in the model, or reducing the order of autoregression. Attempts to overcome the “curse of dimensionality†by using special mathematical methods result in a significant complication of the mathematical apparatus for constructing vector autoregressions, which does not contribute to the expansion of the practice of using vector autoregressions. The article proposes to use for this purpose a step-by-step decomposition method for constructing vector autoregressions of any dimension, which makes the process of constructing these models simple and accessible to any researcher. To test the possibility of using this method in practice, data series on the dynamics of eight main industry indices of the Moscow Exchange were used. At the same time, it was decided to construct a large vector autoregression of the order of p = 10. Using the least squares method, a total of 648 unknown coefficients of this model were estimated. The verification of this model was confirmed by simple autoregressions.