ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 6. Vol. 29. 2023

DOI: 10.17587/it.29.279-283

M. G. Matveev, Dr. Tech. Sc., Professor, E. A. Sirota, Cand. Phys.-Math. Sc., Associate Professor,
Voronezh State University, Voronezh, 394018, Russian Federation

Improving the Quality of Estimates of the Parametric Identification Problem Using the Conservative Condition in Models of Distributed Dynamic Processes

Today the apparatus for modelling non-stationary time series is most in demand in various areas of human activity: meteorology, sociology, medicine, financial market research, and a number of others. The general scientific problem of modelling such series is associated with solving the problem of identification, namely, obtaining such model parameters that would provide a high degree of accuracy and adequacy of the model. However, the problem of bias of least square method (LSM) estimates arises when solving the problem of parametric identification of distributed dynamic processes. There are various possible solutions to this problem. If the time series is trend-stationary, then these may be "ostationation" methods, which are generally difficult to apply. It is possible to use dimensionality reduction methods, but in this case we will still get biased estimates. In our previous works, it was shown that the problem of biased estimates can be solved using the conservativeness condition. The aim of this work was to investigate the possibility of using the conservativeness condition to improve the quality of estimates of the parametric identification problem, as well as to compare these results with the solution of the problem, in the case of applying a filter to it, as well as ridge regression.
Keywords: autoregressive model, finite difference equations, identification, LSM estimates, biased estimates of model parameters, the reduction of the dimensionality, explicit difference scheme, implicit difference scheme, conservativeness condition

P. 279-283

References

1. Guo L. Z., Billing S. A., Coca D. Identification of partial differential equation models for a class of multiscale spatio-temporal dynamical systems, Intr. J. Contr., 2010, no. 83, pp. 1—19.
2. Xun X., Cao J., Mallick B., Carrol R., Maity A. Parameter Estimation of Partial Differential Equation Models, J. Am. Stat. Assoc., 2013, no.108, pp. 1009—1020.
3. Nosko V. P. Econometrics, Moscow, Delo, 2011, 273 p. (in Russian).
4. Matveev M. G., Kopytin A. V., Sirota E. A. Parameters identification of a distributed dynamical model using combined approach, J. Phys. Conf. Ser., 1096 012068, 2018, pp. 1—8.
5. Samarskii A. A. The Theory of Difference Schemes, Moscow, 2001, (Boca Raton: CRC Press), 616 p. (in Russian).
6. Grebenyuk E. A. Methods of analyzing the nonstationary time series with implicit changes in their properties, Autom. Remote Control, 2005, no. 12, pp. 161—164 (in Russian).
7. Matveev M. G., Sirota E. A. Combined models of non-stationary time series with changing states, Bulletin of VSU, series "System analysis and information technologies", 2016, no. 3, pp. 50—61 (in Russian).
8. 8. Matveev M. G., Kopytin A. V., Sirota E. A., Kopytina E. A. Modeling of nonstationary distributed processes on the basis of multidimensional time series, Procedia Engineering, 2017, vol. 201, pp. 511—516.
9. 9. Kopytin A. V., Kopytina E. A., Matveev M. G. Application of the extended Kalman filter for identification of parameters of the distributed dynamic system, Bulletin of VSU, series "System analysis and information technologies", 2018, no. 3, pp. 44—50 (in Russian).
10. 10. Matveev M. G., Sirota E. A., Semenov M. E., Kopytin A. V. Verification of the convective diffusion process based on the analysis of multidimensional time series, CEUR Workshop, 2017, Proc. 2022, pp. 354—358.

To the contents