Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

CivilComp Proceedings
ISSN 17593433 CCP: 84
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 29
The Statistical Significance of Some Numerical Algorithms to Identify Rational Structures in Causal Time Series Models C. GonzálezConcepción, M.C. GilFariña and C. PestanoGabino
Department of Applied Economics, University of La Laguna, Tenerife, Spain C. GonzálezConcepción, M.C. GilFariña, C. PestanoGabino, "The Statistical Significance of Some Numerical Algorithms to Identify Rational Structures in Causal Time Series Models", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Fifth International Conference on Engineering Computational Technology", CivilComp Press, Stirlingshire, UK, Paper 29, 2006. doi:10.4203/ccp.84.29
Keywords: Padé approximation, orthogonal polynomials, numerical methods, time series modelling, economics.
Summary
The systematic study of data to obtain specific properties from long (or short)
data series is a main objective in several sciences. Over the last decades, several
research activities have helped to obtain new procedures and techniques to
characterize dynamic relations associated with data series.
In time series modelling, several authors have considered the use of rational approximation theory in econometric modelling. Consideration is given to both the univariate case (Beguin et al. [2]) and the multivariate case (Berlinet and Francq [3] and Reinsel [11]). Some interesting results have been given for the specific case of a transferfunction model (González et al. [7] and Lii [10]) In this context, several techniques closely related to the Padé approximation and orthogonal polynomials (Baker and GravesMorris [1] and Brezinski [5]) have been proposed to identify possible rational structures. Since the covariance structure of the underlying processes exhibits features related to the order of the models, it is possible to use certain numerical algorithms (corner method, epsilonalgorithm, rsalgorithm, and qdalgorithm) to estimate the unknown orders from observations and expectations. In particular, these methods have been proposed for the study of economic data in different contexts (financial, marketing, farming) (González and Gil [8] and González et al. [9]). This paper is the continuation of previous papers which are concerned with illustrating the application of certain numerical methods for identifying certain rational structures associated with data series. Special emphasis is given here to the study of the statistical significance of two of these numerical methods, namely, the rsalgorithm and the qdalgorithm in terms of their asymptotic standard deviations. Empirical work is carried out in the context of the BoxJenkins [4] guidelines. Both proposals are illustrated for the univariate and multivariate case, considering a simulated ARMA model, a simulated transferfunction model with two inputs, and two economic applications, one for the series M given by Box and Jenkins [4] and Tsay [12] and the second one, the volatility series in the Spanish market modelled by Gil and Alegría [6] and González and Gil [8]. Empirical findings emphasize the role of the statistical significance for the numerical values in the aforementioned algorithms. In general, different possible models will be obtained depending on certain critical values. References
purchase the fulltext of this paper (price £20)
go to the previous paper 
