Journal of Mathematics and Statistics

The Numerical Computation of Rational Structures and Asymptotic Standard Deviations in Causal Time Series Data

Concepción González-Concepción, Mar Candelaria Gil-Fariña and Celina Pestano-Gabino

DOI : 10.3844/jmssp.2009.215.225

Journal of Mathematics and Statistics

Volume 5, Issue 3

Pages 215-225


Problem statement: The specific properties of data series are of primary importance in several sciences. In the field of time series analysis, several researchers have considered the rational approximation theory, particularly the Padé Approximation and Orthogonal Polynomials. Approach: In this study, an approach for the statistical significance of two numerical methods, the r-s and q-d algorithm, was proposed which made possible to identify and compute certain rational structures associated with chronological data. Consideration was given to both univariate and multivariate cases. Results: Both algorithms were illustrated empirically through the use of simulated ARMA and TF models and economic data, some of which were taken from previous studies to compare results. Conclusion: This study highlighted the usefulness of several numerical methods (which were all closely related to the PA and OP) in identifying the rational structures associated with data series.


© 2009 Concepción González-Concepción, Mar Candelaria Gil-Fariña and Celina Pestano-Gabino. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.