Choice of the order of the regression model for forecasting of random non-stationary economic processes

Abstract

The object of research is heteroskedastic processes that affect the production of military goods of exporting countries. Today, armed conflicts are the most significant factor affecting the volume of production and export of weapons, since it assumes that the parties have the necessary quantity of weapons and is, in a sense, a stochastic process. The work is devoted to forecasting stochastic effects on the production processes of military goods of exporting countries. As an example, an economic system with stochastic effects and bottleneck problems in production units is considered. The model of the output process is presented as a random process with slow non-stationarity (heteroscedastic process). The methods for predicting non-stationary random processes are used. The problem of choosing and substantiating a mathematical model for predicting a heteroskedastic process is investigated, and considered. It is proved that the most capable short-term forecasting method is the Pade approximation method. It is shown that the Pade method, in fact, is a method of approximation by analytical (finely rational) functions, therefore it can be interpreted as a method of constructing a model of autoregression and moving average (ARIMA). Modifications of the ARIMA model, such as a model of autoregression and integrated moving average or autoregression and fractal integrated moving average, are considered. A modified method is developed for choosing the order of the autoregressive model according to the Akaike information criterion and beyond the Bayesian information criterion. The model problems and examples of experimental dependencies are analyzed. An effective technique is proposed for choosing the order of regression models used in the practical forecasting of stochastic processes, based on the canonical layouts of a random function. To partition the distribution function into non-equidistant intervals with constant flow intensities, an economic recurrence algorithm is used. The calculation results can be used to optimally select the order of the regression model, which approximates the real production process in the form of a time series with random external influences.