Control Systems and Computers

DOI: https://doi.org/10.15407/usim.2016.01.003

Upr. sist. maš., 2016, Issue 1 (261), pp. 3-15.

UDC 519.25:681.5

Sarychev Alexander P., Doctor (Eng.), Institute of techn. mechanics of NAS and NCA of Ukraine (Dnepropetrovsk), E-mail: Sarychev@prognoz.dp.ua

Linear Autoregression with Random Coefficients Based on the Group Method of Data Handling in Conditions of Quasirepeated Observations

Introduction and purpose: The linear autoregression equation is traditional mathematical object in the theory and practice of the Group Method of Data Handling (GMDH). In 80-th years of the last century academician O.G. Ivakhnenko often posed such tasks in connection with so-called “the objective system analysis (OSA)” and then, as a rule, as criterion of selection of models (parameter of quality of regression equation) the criterion of regularity of GMDH was applied. The developed criterion is the criterion of regularity which is constructed with dividing of observations on training and testing subsamples in conditions of quasirepeated observations.

Methods: Object of research is process of modelling in a class of autoregression equations in conditions of uncertainty on structure of regressors. In this theoretical article we used the multivariate statistical analysis, the regression analysis, the theory of matrixes, the mathematical analysis and the Group Method of Data Handling.

Results: For modeling in a class of autoregression equations the criterion of regularity with dividing of observation sample on training and testing subsamples in conditions of quasirepeated observations is offered. It is proved, that the optimum set of regressors exists. The condition of a reduction of optimal autoregression equation is obtained. This condition depends on parameters of autoregression equation and volumes of samples.

Conclusion: The developed criterion of regularity allows solving a problem of structural identification in a class of autoregression equations in conditions of quasirepeated observations and can be recommended at the decision of various scientific and practical problems.

Download full text! (In Russian).

Keywords: structural uncertainty, criterion of regulatory, autoregression, GMDH.

1. Sovremennyye metody identifikatsii sistem. M.: Mir, 1983. 400 p. (In Russian).
2. Silvestrov, A.N., Chinayev, P.I., 1987. Identifikatsiya i optimizatsiya avtomaticheskikh sistem. M.:Energoatomizdat, 199 p. (In Russian).
3. Lyung, L., 1991. Identifikatsiya sistem. Teoriya dlya pol’zovatelya. M.: Nauka, 432 p.
4. Green, W.H., 2002. Econometric Analysis. New Jersey: Pearson Education, Inc., 1056 p.
5. Söderström, T., Soverini, U., Mahata, K., 2002. “Perspectives on errors-in-variables estimation for dynamic systems”. Signal Processing, 82 (8), pp. 1139–1154.
   https://doi.org/10.1016/S0165-1684(02)00252-9
6. Kuntsevich, V.M., 2006. Upravleniye v usloviyakh neopredelennosti: garantirovannyye rezultaty v zadachakh upravleniya i identifikatsii. K.: Nauk. dumka, 264 p. (In Russian).
7. Markovsky, I., Van Huffel, S., 2007. “Overview of total least squares methods”. Signal Processing, 87, pp. 2283–2302.
   https://doi.org/10.1016/j.sigpro.2007.04.004
8. Söderström, T., 2007. “Errors-in-variables methods in system identification”. Automatica, 43 (6), pp. 939–958.
   https://doi.org/10.1016/j.automatica.2006.11.025
9. Ivakhnenko, A.G., 1982. Inductive method of self-organization of complex systems.Kiev: Naukova dumka, 296 p. (In Russian).
10. Self-organizing methods in modelling: GMDH type algorithms. New York, Basel: Marcel Decker Inc., 1984, 350 p.
11. Ivakhnenko, A.G., Stepashko, V.S., 1985. Noise-immunity of modeling. Kiev: Naukova dumka, 216 p. (In Russian).
12. Ivakhnenko, A.G., Muller, J.A., 1985. Self-organization of forecasting models. Kiev: Tekhnika, 223 p. (In Russian).
13. Ivakhnenko, A.G., Yurachkovskiy, Yu.P., 1987. Modeling of complex systems from experimental data. Moscow: Radio i svyaz, 120 p. (In Russian).
14. Madala, H.R., Ivakhnenko A.G., 1994. Inductive Learning Algorithms for Complex System Modeling. London, Tokyo: CRC Press Inc., 370 p.
15. Muller, J.-A., Lemke, F., 2000. Self-organizing Data Mining. Extracting Knowledge from Data. Hamburg: Libri, 250 p.
16. Sarychev A.P., 2008. Identifikatsiya sostoyaniy strukturnoneopredelennykh sistem. Dnepropetrovsk: Institut tekhnicheskoy mekhaniki NAN i NKA Ukrainy, 268 p. (In Russian).
17. Sarychev, A.P., 2013. Identifikatsiya parametrov sistem avtoregressionnykh uravneniy so sluchaynymi koeffitsiyentami pri izvestnykh kovariatsionnykh matritsakh. Problemy upravleniya i informatiki, 5, pp. 33–52. (In Russian).
18. Seber, Dzh., 1980. Lineynyy regressionnyy analiz. M.: Mir, 456 p. (In Russian).
19. Yermakov, S.M., Zhiglyavskiy, A.A., 1987. Matematicheskaya teoriya optimal’nogo eksperimenta. M.: Nauka, 320 p. (In Russian).
20. Sarychev, A.P., 2913. “Modelirovaniye v klasse sistem regressionnykh uravneniy na osnove metoda gruppovogo ucheta argumentov”. Problemy upravleniya i informatiki, 2, pp. 8–24. (In Russian).
21. Sarychev, A.P., 2014. “Modelirovaniye v klasse sistem regressionnykh uravneniy so sluchaynymi koef­fitsiyentami na osnove metoda gruppovogo ucheta argumentov”. Inductive modeling of complex systems, K .: IRTC ITandS NASU, 6, pp. 137–156. (In Russian).
22. Sarychev, A.P., 2015. “Modelirovaniye v klasse sistem avtoregressionnykh uravneniy v usloviyakh strukturnoy neopredelennosti”. Problemy upravleniya i informatiki, 4, pp. 79–103. (In Russian).

Recieved 09.04.2015