Modeling of complex processes using autoregressive methods

We reviewed the use of numerical series to estimate the parameters in the autoregressive model in this paper. A method and the basic procedure for determining the order of autoregressive model and the choice of a numerical series are described. The purpose of this work is the generalization of the obtained results, identifying characteristics of the autoregressive when modeling complex processes and simplified procedures for the selection of parameters is based on the use of numerical series. The basic theoretical and practical results are obtained on the basis of methodology of system analysis, the theory of random processes, information technologies and methods of fundamental and applied mathematics. We compared the method of numerical series with known methods ofparameter estimation in autoregressive models. It is shown the relationship between the autoregressive models and classical mathematical concepts such as the ‘golden section’, ‘Pascal's triangle ’, the Fibonacci numbers and the Tribonacci numbers. Also we gave estimates for autoregressive models for long-term forecasting. It is shown the relationship between the fourth-order autoregressive with the series of the Kvadrobonacci numbers. We summarized the known recommendations on the application of numerical series. These recommendations help to simplify the procedure for selection of numerical series and improve the quality of the model. For short and medium-term forecasts with a constant average it is recommended to use coefficients which are calculated using the Fibonacci and the Tribonacci series. The obtained results will be useful in modeling of complex processes with a time component.