Multicriteria method for identification and forecasting

G. K. Kamenev

Matematičeskoe modelirovanie, Tome 29 (2017) no. 8, pp. 29-43.

Résumé

The multicritera approach to identification and forecasting for mathematical models is considered. The need for such an approach arises, in particular, when it is required to take into account the errors that cannot be reduced to one function, and in the absence of specific information about the data interference class. Paper is devoted to the multicritera version of the Identification Sets Method based on approximation and visualization of the identification errors vector-function graph and its projections on identification parameters space. The nearness function for criterion point proximity to the set of nonimprovable (Pareto efficient) identification solutions is defined. The efficient criteria set, efficient and sub-efficient parameters sets and corresponding forecasting trajectories tubes are explored. To construct these objects we use methods for approximation of implicitly specified sets, in particular, methods for approximation the Edgeworth–Pareto hull and the deep holes method. The technique and examples for the case of two identification criteria are considered in detail.

Détail

Keywords: parameters identification, forecast, robustness, multicriteria decision making, Egdeworth–Pareto hull, efficient and subefficient solutions, methods for approximation of implicitly specified sets, identification sets method, interactive decision maps.
Mots-clés : efficient set, Pareto frontier

Bibliographie

[1] Krasnoshchokov P. S., Petrov A. A., Printsipy postroeniia modelei, FAZIS, VTS RAN, M., 2000

[2] Ljung L., System Identification: Theory for User, Prentice-Hall, Inc., 1987 | MR | Zbl

[3] Kamenev G. K., “Multicriteria Identification Sets Method”, Comput. Maths. Math. Phys., 56:11 (2016), 1843–1858 | DOI | DOI | MR | Zbl

[4] Kamenev G. K., “A Visual Method for Parameter Estimation”, Doklady Mathematics, 57:2 (1998), 305–307 | MR | Zbl

[5] Kamenev G. K., “Ob odnom podchode k issledovaniiu neopredelennosti, voznikaiushchei pri identifokazii modelei”, Matematicheskoe modelirovanie, 22:9 (2010), 116–128 | Zbl

[6] Kamenev G. K., Metod issledovaniia neopredelennosti, voznikaiushchei pri identifikazii parametrov modelei, Izd. VTS RAN, M., 2010, 46 pp.

[7] Berezkin V. E., Kamenev G. K., Lotov A. V., “Hybrid Adaptive Methods for Approximating a Nonconvex Multidimensional Pareto Frontier”, Comput. Maths. Math. Phys., 46:11 (2006), 1918–1931 | DOI | MR

[8] Bushenkov V. A., Chernykh O. L., Kamenev G. K., Lotov A. V., “Multidimensional Images Given by Mappings: Construction and Visualization”, Pattern Recognition and Image Analysis, 5:1 (1995), 35–56

[9] Lotov A. V., Bushenkov V. A., Kamenev G. K., Chernykh O. L., Kompiuter i poisk kompromissa. Metod dostizhimykh zelei, Nauka, M., 1997, 239 pp.

[10] Lotov A. V., Bushenkov V. A., Kamenev G. K., Interactive Decision Maps. Approximation and Visualization of Pareto Frontier, Appl. Optimization, 89, Kluwer Academic Publishers, Boston–Dordrecht–New York–London, 2004, 310 pp. | DOI | MR | Zbl

[11] Kamenev G. K., “Approximation of Completely Bounded Sets by the Deep Holes Method”, Comput. Math. Math. Phys., 41:11 (2001), 1667–1675 | MR | Zbl

[12] Andreev M. Iu., Vrzheshch V. P., Pilnik N. P., Pospelov I. G., Khokhlov M. A., Zhukova A. A., Radionov S. A., “Model mezhvremennogo ravnovesiia ekonomiki Rossii, osnovannaia na dezagregirovanii makroekonomicheskogo balansa”, Tr. sem. im. I.G. Petrovskogo, Izd-vo Mosk. Un-ta, M., 2013, 43–145

[13] Kamenev G. K., Olenev N. N., “Study of the Russian Economy's Identification and Forecast Stability Using a Ramsey Type Model”, Mathematical Models and Computer Simulations, 7:2 (2015), 179–189 | DOI | MR