ALGORITHMS FOR RESEARCH OF MULTIDIMENSIONAL TIME SERIES TAKING INTO ACCOUNT THE EXTENDED INFLUENCE OF FACTORS ON THE BASIS OF MATHEMATICAL MODELING

The models and methods of neural network modeling of dynamics based on the analysis of multidimensional time series, taking into account the delayed influence of significant factors, are investigated. In connection with the impossibility of simultaneous determination of the optimal time lag and network training, it is necessary to consider finding a multidimensional lag as a separate optimization problem. The mathematical formulation of the problem of building a neural network for a non-zero delay is described, a description of the optimization characteristics of the latency for one independent variable (input) is given, the information base for modeling and forecasting and neural network data processing algorithms are specified, and the latency vector for significant factors is optimized. The fundamental possibility of using sensitivity analysis to find the optimal multidimensional time lag was confirmed during the computational experiment. The sensitivity analysis was carried out on test data obtained by calculating the values of the sets of functions of several variables with a known delay for some variables. Analysis of learning errors, generalization and forecasting on the original and offset series allowed to conclude that there was a significant decrease in the training error and prediction error on the shifted series with a practically unchanged generalization error, which indicates the effectiveness of the proposed algorithm and the absence of structural effects in changing the quality of the forecast.

1. Kryuchkova I.N. Spetsial'noe matematicheskoe obespechenie kratkosrochnogo prognozirovaniya na osnove neyrosetevogo modelirovaniya i analiza mnogomernogo laga: Avtoref. dis. … kand. tekhn. nauk. Voronezh, 2007.

2. Avdeeva V.M., Kravets O.Ya. Teoreticheskie osnovy prognozirovaniya nalogovykh postupleniy na osnove krosskorrelyatsionnogo analiza mnogomernykh vremennykh ryadov// Sistemy upravleniya i informatsionnye tekhnologii, 2006, No.1.2(23). - pp. 212-216.

3. Avdeeva V.M., Kravets O.Ya., Kryuchkova I.N. Territorial'noe prognozirovanie nalogovykh postupleniy s primeneniem mnogomernykh krosskorrelyatsionnykh tekhnologiy// Innovatsionnyy Vestnik Region, 2007, No.3(9). - pp. 31-36.

4. Avdeeva V.M., Kryuchkova I.N. Issledovanie tekhnologii neyrosetevogo prognozirovaniya nalogovykh postupleniy territorii s primeneniem tekhniki mnogomernogo krosskorrelyatsionnogo analiza// Territoriya nauki, 2007, No.4(5). - pp. 428-436.

5. Hecht-Nielsen R. Theory of the Backpropagation Neural Network// Neural Networks, 1989, 1(1):593 - 605.

6. Gibbs M.N. Variational Gaussian process classifiers// IEEE Transactions on Neural Networks, 2000, 11 (6): 1458-1464.

7. Deep Learning/ I. Goodfellow, Y. Bengio, A. Courville. MIT Press, 2016, 196 p.

8. Galushkin A.I. O metodike resheniya zadach v neyrosetevom logicheskom bazise// Neyroinformatika – 2006. Chast' 1. https://refdb.ru/download/1480079.html.