Title: Parameter estimation through the weighted goal programming model

Authors: Belaid Aouni; Cinzia Colapinto; Davide La Torre

Addresses: Management and Marketing Department, College of Business and Economics, Qatar University, P.P. Box 2713, Doha, Qatar ' Department of Management, Ca' Foscari University of Venice, San Giobbe – Cannaregio 873 – 30121 Venice, Italy ' Department of Economics, Management and Quantitative Methods, University of Milan, Milan, Italy; Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi, UAE

Abstract: Many models in economics, management and finance can be described in terms of nonlinear dynamical systems which usually depend on some unknown parameters. To conduct a long-run behaviour analysis of these models it is of paramount importance to establish efficient and accurate parameter estimation techniques. Today many sophisticated nonlinear model estimation, selection and testing approaches are available and reliable. However, when the nonlinear dynamical systems take the form of differential equations, many of them fail and it is required to use more advanced techniques. The aim of this paper is to present a weighted goal programming formulation for estimating the unknown parameters of dynamical models described in terms of differential equations. The method is illustrated through two different applications to population dynamics (Malthus model) and innovation diffusion (Bass model).

Keywords: parameter estimation; weighted goal programming; modelling; Malthus model; Bass model; nonlinear systems; differential equations; unknown parameters; dynamical models; population dynamics; innovation diffusion.

DOI: 10.1504/IJMCDM.2015.071251

International Journal of Multicriteria Decision Making, 2015 Vol.5 No.3, pp.263 - 273

Received: 06 Mar 2014
Accepted: 22 Nov 2014

Published online: 18 Aug 2015 *

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