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PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
The Statistical Significance of Some Numerical Algorithms to Identify Rational Structures in Causal Time Series Models
C. González-Concepción, M.C. Gil-Fariña and C. Pestano-Gabino
Department of Applied Economics, University of La Laguna, Tenerife, Spain
C. González-Concepción, M.C. Gil-Fariña, C. Pestano-Gabino, "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", Civil-Comp Press, Stirlingshire, UK, Paper 29, 2006. doi:10.4203/ccp.84.29
Keywords: Padé approximation, orthogonal polynomials, numerical methods, time series modelling, economics.
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. ) and the multivariate case (Berlinet and Francq  and Reinsel ). Some interesting results have been given for the specific case of a transfer-function model (González et al.  and Lii )
In this context, several techniques closely related to the Padé approximation and orthogonal polynomials (Baker and Graves-Morris  and Brezinski ) 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, epsilon-algorithm, rs-algorithm, and qd-algorithm) 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  and González et al. ).
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 rs-algorithm and the qd-algorithm in terms of their asymptotic standard deviations.
Empirical work is carried out in the context of the Box-Jenkins  guidelines. Both proposals are illustrated for the univariate and multivariate case, considering a simulated ARMA model, a simulated transfer-function model with two inputs, and two economic applications, one for the series M given by Box and Jenkins  and Tsay  and the second one, the volatility series in the Spanish market modelled by Gil and Alegría  and González and Gil .
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.
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