Structural Identification of Systems with Distributed Lag

Full Text (PDF, 514KB), PP.1-10

Views: 0 Downloads: 0


Nikolay Karabutov 1,*

1. Dept. of Problems Control, Moscow State Engineering University of Radio Engineering, Electronics and Automation, Dept. of Mathematics, Financial University under the Government of the Russian Federation, Moscow, Russia

* Corresponding author.


Received: 3 Feb. 2013 / Revised: 11 May 2013 / Accepted: 5 Aug. 2013 / Published: 8 Oct. 2013

Index Terms

Structural Identification, Distributed Lag, Virtual Portrait, Decision-Making, Parametrical Identification


The problem of structural identification of systems with the distributed lag in the conditions of uncertainty is considered. Known statistical approaches are laborious and not always allow making the decision on lag structure. Therefore in work for the problem decision the special class of static structures (SS) (virtual portraits) explored system is introduced. Process of the decision of a problem consists of two steps. At the first step set of secants for initial system is under construction. Completeness of set of secants is a sign of linearity of system. Nonfulfilment of conditions of completeness is a sign of nonlinearity of system. Estimation of nonlinearity of system execute on an indicator of level of nonlinearity of the system, offered in work. At the second step the special structural space is introduced and is defined SS for a nonlinear part of system. The estimation of nonlinear properties of system is executed on the basis of identification of parameters of set of secants SS. Criteria and algorithms of decision-making on structure of a lag on the basis of the analysis of virtual portraits are offered. The analogue of criterion of Durbin-Watson is offered. The received results are generalized on a case of the distributed lag in input and output variables of system. It is shown that to structural identification of systems with the distributed lag we will not apply the analysis of sector sets. The approach to parametrical identification of system with the distributed lag in the conditions of uncertainty is offered.

Cite This Paper

Nikolay Karabutov, "Structural Identification of Systems with Distributed Lag", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.11, pp.1-10, 2013. DOI:10.5815/ijisa.2013.11.01


[1]Malinvaud, E. Statistical methods in econometrics. 3d ed. North-Holland Publishing Co, Amsterdam, 1980.

[2]Johnston J. Econometric methods. 2nd edition. McGraw-Hill Book Company, New York, 1972.

[3]Demetriou I. C., Vassiliou E. E. An algorithm for distributed lag estimation subject to piecewise monotonic coefficients. International Journal of Applied Mathematics, v39, n1, 2009, pp. 1-10.

[4]Dhrymes, P.J. Distributed Lags: Problems of Esti-mation and Formulation. Holden-Day, San Fran-cisco. 1971.

[5]Gershenfeld, N., The Nature of Mathematical Modelling. Cambridge University Press, Cambridge, 1999.

[6]Kailath, T. (editor), Linear Least-Squares Estima-tion, Stroudsburg, Pennsylvania: Dowden, Hutchinson and Ross, Inc., Benchmark Papers in Electrical Engineering and Computer Science, V17, 1977.

[7]Karabutov, N.N. Structural identification of sys-tems: the analysis of informational structures, URSS, Librokom, Moscow, 2009. (in Russia).

[8]Armstrong, B. Models for the relationship between ambient temperature and daily mortality. Epidemiology, v17(6), 2006, pp. 624-631.

[9]Nelson, C. R. Schwert, G.W. Estimating the pa-rameters of a distributed lag model from cross-section data: The case of hospital admissions and discharges. Journal of the American Statistical As-sociation, v69, n347, 1974, pp. 627-633.

[10]Gasparrini A., Armstrong B., Kenwardb M. G. Distributed lag non-linear models. Statistics in Medicine, v29(21), 2010, pp. 2224–2234.

[11]Fisher, I. Note on a Short-cut Method for Calculat-ing Distributed Lags. Bulletin de l’Institut Interna-tional de Statistique, v29, 1937.

[12]Коуск, L. M., Distributed Lags and Investment Analysis, North-Holland Publishing Company, Amsterdam, 1954.

[13]Almоn, S. The distributed lag between capital ap-propriations and expenditures, Econometrica, v33, 1965, pp. 178-196.

[14]Theil, H., Stern, R. M., A simple unimodal lag distribution. Metroeconomica, v12, 1960, pp. 111–119.

[15]Solow, R. On a family of lag distributions. Econ-ometrica, v28, 1960, pp. 393-406.

[16]Jоrgensоn, D. W. Minimum variance, linear, unbi-ased seasonal adjustment of economic time series. Journal of the American Statistical Association, v59, n307, 1964, pp. 681-724.

[17]Demetriou I. C., E. E. Vassiliou. A distributed lag estimator with piecewise monotonic coefficients. Proceedings of the world congress on engineering. 2008, v2, WCE 2008, July 2 - 4, 2008, London, U.K.

[18]Yoder J. Autoregressive distributed lag models. WSU Econometrics II, 2007, pp. 91-115.

[19]Cheng Hsiao. Analysis of Panel Data. Cambridge University Press, 2003.

[20]Wen-Jen Tsay. The long memory autoregressive distributed lag model and its application on con-gressional approval. Institute of Economics, Aca-demia Sinica, 2005.

[21]Carter R. A. L., Zellner A., The arar error model for univariate time series and distributed lag models.

[22]Lansing K. J. Real-time estimation of trend output and the illusion of interest rate smoothing. FRBSF economic Review, 2002, pp. 18-34.

[23]Duffee Gr. R. Term structure estimation without using latent factors. Haas School of Business Uni-versity of California-Berkeley, 2005.

[24]Campos J., Ericsson N. R., and Hendry D. F. Gen-eral-to-specific modeling An overview and selected bibliography. International finance discussion papers, n838, 2005.

[25]Hansen B.E. Econometrics. University of Wiscon-sin, 2013.

[26]Alessi L., Barigozzi M. and Capasso M. A robust criterion for determining the number of static fac-tors in approximate factor models. Working paper series, n903, 2008.

[27]Castle, J.L., Doornik, J.A., and Hendry, D.F. Eval-uating automatic model selection. (Discussion pa-per series, 474) (workingPaper) Economists Online, 2010.

[28]Karabutov N.N. Structural identification of static systems with distributed lags. International journal of control science and engineering, v2012, n2(6), pp. 136-142.

[29]Karabutov, N.N. Structural identification of static plants: Fields, structures, methods, URSS, Libro-kom, Moscow, 2011.

[30]Karabutov N.N. Structures, fields and methods of identification of nonlinear static systems in the conditions of uncertainty. Intelligent Control and Automation, v1, 2010, pp. 59-67.

[31]Karabutov N.N. Adaptive algorithms for structural parameters identification of single-valued nonline-arities of static systems with a vectorial input. Int. J. Sensing, Computing and Control, v2, n1, 2012, pp. 1-11,

[32]Shilov, G. Mathematical analysis. Fizmathlit, Moscow 1961. (in Russia).

[33]Lyapunov, A.M., General problem about a move-ment stability. State publishing house of techniko-theoretical literature, Moscow, 1950.

[34]Karabutov N.N. adaptive identification of systems. Information synthesis. URSS, Librokom, Moscow, 2006.