Complex-Valued Autoregression in Economic Forecasting of One-Dimensional Series

Abstract

Autoregressive models AR(p) and their numerous modifications are actively used for short-term forecasting of economic processes. At the same time, it is not always possible to achieve the necessary forecast accuracy; therefore, scientists engaged in economic forecasting continue to develop new methods and approaches in order to use them to improve the accuracy of their forecasts. One of the promising approaches in this direction is associated with the use of elements of the theory of functions of a complex variable in modeling the economy (complex-valued economy). The article shows how, using complex-valued autoregressive models, to increase the accuracy of short-term economic forecasting. Here, the properties and the possibility of practical application in short-term economic forecasting of two models are considered: the complex-valued autoregression model, the real part of which is the predicted indicator, and the imaginary part is the time at which this indicator was observed (model CTAR(p)) and the model, the real part of which is the predicted indicator, and the imaginary part is the current forecast error CARE(p). It is shown that the classical model of autoregression of real variables AR(p) is a special case of each of these two models. The main focus of the article is on studying the properties of the ReCARE(p) model. It is theoretically substantiated that this model predicts short-term economic dynamics more accurately than the AR(p) model. And it is shown on practical examples. Therefore, in cases, where autoregressive models are appropriate, it is recommended to use the new ReCARE(p) model, as it is more accurate. It is shown that, on the platform of this basic model, it is possible to develop new short-term forecasting models similar to the ARMA(p, q) and ARIMA(p, q) models, from which one should expect increased accuracy of short-term economic models.