Research Article Open Access

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

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

Abstract

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.

Journal of Mathematics and Statistics
Volume 5 No. 3, 2009, 215-225

DOI: https://doi.org/10.3844/jmssp.2009.215.225

Submitted On: 29 October 2008 Published On: 30 September 2009

How to Cite: González-Concepción, C., Gil-Fariña, M. C. & Pestano-Gabino, C. (2009). The Numerical Computation of Rational Structures and Asymptotic Standard Deviations in Causal Time Series Data . Journal of Mathematics and Statistics, 5(3), 215-225. https://doi.org/10.3844/jmssp.2009.215.225

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Keywords

  • Padé approximation
  • orthogonal polynomials
  • numerical methods
  • asymptotic deviation
  • time series modeling
  • economics